__PAPERS__

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*1970-1979*

- "On
the Baire System Generated by a Linear Lattice
of Functions,"
__Fundamenta____Mathematicae__68(1970), 51-59. - "Sigma-ideals
and Related Baire Systems,"
__Fundamenta____Mathematicae__71(1971), 171-178. - "Some
Examples of Sigma-ideals and Related Baire
Systems,"
__Fundamenta____Mathematicae__71(1971), 179-184. - "On
the Stieltjes Integrability
of Dense Subsets of C[a,b],"
__Revue Roumaine de Mathematiques Pures et Appliquees__17(1972), 1623-1624. - "A
Representation Theorem of the 2nd Dual of C[0,1],"
__Studia____Mathematica__46(1973), 197-200. - "On
Borel Measures and Baire's
Class 3," Proceedings American Mathematical Societyá39(1973),
308-312.
- "The
Baire Order of the Functions Continuous Almost
Everywhere,"
__Proceedings American Mathematical Society__41(1973), 535-540. - "On
Sets Generated by Rectangles," (with R.H. Bing and W.W. Bledsoe)
__Pacific Journal of Mathematics__51(1974), 27-36. - "Baire Functions, Borel Sets
and Ordinary Function Systems,"
__Advances in Mathematics__12(1974), 418-450. - "The
Baire Order of the Functions Continuous Almost
Everywhere, II," Proceedings American Mathematical Society 51(1975),
371-377.
- "The
Continuum Hypothesis, Integration and Duals of Measure Spaces,"
__Illinois Journal of Mathematics__19(1975), 34-40. - "Homeomorphisms
of the Plane," (with B.L. Brechner),
__Pacific Journal of Mathematics__59(1975), 375-381. - "Countably Generated Families," Proceedings
American Mathematical Society 54(1976), 291-297.
- "On
Non-isomorphic Analytic Sets," Proceedings American Mathematical
Society 58(1976), 241-244.
- "On
Non-isomorphic Projective Sets,"
__Mathematika__, 23(1976), 151-155. propties of sets defined by restrictions on thier exapansions in various bases - the see paper by Mauldin and williams in the TAMS - "The
Non-Existence of Certain Invariant Measures," (with P. Erdos)
__Proceedings American Mathematical Society__59(1976), 321-322. - "EC+
Homeomorphisms of Euclidean Spaces," (with B. Brechner),
__Topology Proceedings__, 1(1976), 335-343. - "On
Rectangles and Countably Generated
Families,"
__Fundamenta____Mathematicae__, 95(1977), 129-139. - "Some
Effects of Set-Theoretical Assumptions in Measure Theory,"
__Advances in Mathematics__27(1978), 45-62. - "The
Boundedness of the Cantor-Bendixson
Order of Certain Analytic Sets," P
__acific Journal of Mathematics__74(1978), 167-177. - "A
Cross Section Theorem and an Application to C*-Algebras," (with
R.R. Kallman),
__Proceedings American Mathematical Society__69(1978), 57-61. - "Measurable
Parametrizations and Selections," (with D. Cenzer), Transactions American Mathematical Society
245(1978), 399-408.
- "The
Existence of Non-measurable Sets," American Mathematical Monthly
87(1979), 45-46.
- "Borel Parametrizations,"
Transactions American Mathematical Society 250(1979), 223-234.
- "The
Set of Continuous Nowhere Differentiable Functions,"
__Pacific Journal of Mathematics__83(1979), 199-205. Correction, Pacific. J. Math. 121(1986), 110-111.

*1980-1989*

- "Rotations
of the Circle," (with P. Erdos),
Lecture Notes in Mathematics, Measure Theory, Oberwolfach
1979, Vol. 794, Springer-Verlag, Heidelberg,
1980, 53-56.
- "Some
Selection Theorems and Problems," Lecture Notes in Mathematics,
Measure Theory, Oberwolfach 1979, Vol. 794,
Springer-Verlag, Heidelberg, l980, 160-165.
- "On
Positively Regular Homeomorphisms of Euclidean Spaces," (with
B.L. Brechner),
__General Topolog__propties of sets defined by restrictions on thier exapansions in various bases - the see paper by Mauldin and williams in the TAMS__y and Its Applications__, 11(1980), 232-242. - "Faithful
Extensions of Analytic Sets to Borel Sets,"
(with D. Cenzer),
__Houston Journal of Mathematics__6(1980), 19-29. - "Inductive
Definability: Measure and Category," (with D. Cenzer),
__Advances in Mathematics__, 38(1980), 55-90. - "On
the Borel Subspaces of Algebraic
Structures,"
__Indiana University Mathematical Journal__29(1980), 161-165. - "Bimeasurable Functions," Proceedings American
Mathematical Society 83(1981), 369-371.
- "Continuous
One-to-One Parametrizations," (with H. Sarbadhikari),
__Bulletin des Sciences Mathematiques__, 105(1981), 435-444. - "Some
Additive Properties of Sets of Real Numbers," (with P. Erdos and K. Kunen),
__Fundamenta____Mathematicae__, 113(1981), 187-199. - "Conditional
Distributions and Orthogonal Measures," (with J.P. Burgess), Annals
of Probability, 9(1981), 902-906.
- "Parametrizations of Coanalytic
Sets with Relatively Nonmeager Sections,"
(with S. Srivastava),
__Comptes____Rendus de l'academie des Sciences__, Paris, Series I, 292(l981), 743-745. - "Realizations
of Maps," (with A.H. Stone),
__Michigan Journal of Mathematics__, 28(1981), 369-374. - "Projective
Well-orderings and Extensions of Lebesgue
Measure,"
__Colloquium Mathematicum__, 46(2) (1982), 185-188. - "One-to-One
Selections - Marriage Theorems," American Journal of Mathematics,
104(1982), 823-828.
- "On
the Borel Class of the Derived Set
Operator," (with D. Cenzer),
__Bulletin Societe Mathematiques France__, 110(4) (1982), 357-380. - "Realizations
of Maps," (with A.H. Stone), Lecture Notes in Mathematics,
__Measure Theory__, Oberwolfach 1981, Vol. 945, Springer-Verlag, Heidelberg, 1982, 145-149. - "A
Survey of Problems and Results Concerning Orthogonal Transition
Kernels," (with D. Preiss and H.v. Weizsäcker), Lecture
Notes in Mathematics,
__Measure Theory__, Oberwolfach l981, Vol 945, Springer-Verlag, Heidelberg, 1982, 419-424. - Editor,
__The____Scottish Book__, Birkhauser-Boston, Inc., Boston, Mass., 1982, 281 pages. - "The Generalized Riemann
Integral," by R. M. McLeod, book review,
__Mathematical Intelligencer__, 4(4) (1982), 197-198. - "On
the Hausdorff Dimension of a Set of Continued
Fractions," (with R.J. Gardner),
__Illinois Journal of M__propties of sets defined by restrictions on thier exapansions in various bases - the see paper by Mauldin and williams in the TAMS__athematics__, 27(2) (1983), 334-345. - "Measurable
Representations of Preference Orders," Transactions American
Mathematical Society 275(2) (1983), 761-769.
- "Orthogonal
Transition Kernels," (with D. Preiss and H.v. Weizsacker),
Annals of Probability, 11(4) (1983), 970-988.
- "Representations
of Well-Founded Preference Orders," (with D. Cenzer),
__Canadian Journal of Mathematics__, 35(3) (1983), 496-508. - "On
the Borel Class of the Derived Set Operator
II," (with D. Cenzer),
__Bulletin Societe Mathematiques France__, 111(1983), 367-372. - "Problem
24 of the Scottish Book," (with I. Labuda),
__Colloquium Mathematicum__, 48(1) (1984), 89-91. - "Random
Homeomorphisms," (with S. Graf and S. Williams), Lecture Notes in
Mathematics,
__Measure Theory__, Oberwolfach 1983, Vol. 1089, Springer-Verlag, Heidelberg, 1984, 23-26. - "Borel Equivalence and Isomorphism of Coanalytic Sets," (with D. Cenzer)
__Dissertationes____Mathematicae (=Rozprawy Matematyczne)__CCXXVIII(1984), 32 pages. - "A
Parametrization Theorem," (with G. Magerl and E. Michael),
__Topology and Its Applications__, 21(l985), 87-94. - "Measurable
One-to-One Selections and Transition Kernels," (with S. Graf),
American Journal of Mathematics, 107(2) (1985), 407-426.
- "Ulam's Redistribution of Energy Problem: Collision
Transformations," (with D. Blackwell),
__Letters in Mathematical Physics__10(l985), 149-153. - "Random
Homeomorphisms," (with S. Graf and S. Williams),
__Advances in Mathematics__, 60(1986), 239-359. - "Shift Maximal Sequences:
Existence, Uniqueness and Multiplicity," (with W.A. Beyer and P.R.
Stein), Los Alamos Report LA-UR-84-2507,
__Journal of Mathematics and its Applications__115(1986), 305-362. - "Coalition
Convex Preference Orders Are Almost Surely Convex,"
__Journal of Mathematics and its Applications__114(1986), 548-551. - "Random
Recursive Constructions: Asymptotic Geometric and Topological
Properties" (with S. Williams), Transactions American Mathematical
Society 295(1986), 325-346.
- "On
the Hausdorff Dimension of Some Graphs,"
(with S. C. Williams), Transactions American Mathematical Society 298 (2)
(1986), 793-803.
- "On the Hausdorff Dimension of Graphs and Random Recursive
Objects,"
__Dimensions and Entropies in Chaotic Systems, Quantification of Complex Behavior__, Edited by G. Mayer-Kress, Springer-Verlag, New York, 1986, 28-33. - "Problems
and Games in Mathematics," (with S.M. Ulam),
__Advances in Applied Mathematics__8(1987), 281-344. - "The
Exact Hausdorff Dimension in Random Recursive
Constructions," (with S. Graf and S.C. Williams),
__Proceedings National Academy Science__84(1987), 3959-3961. - "The
Volume Common to Two Congruent Circular Cones," (with W. Beyer,
R. Fawcett, B. Swartz), Los Alamos Report LA-UR-84-2654,
__Journal of Symbolic Computations__4(1987), 381-390. - "The Exact Hausdorff Dimension in Random Recursive
Constructions," (with S. Graf and S.C. Williams),
__Memoirs American Mathematical Society__, Volume 381, 1988, 126 pages. - "Bijections of
*R*^{n}Onto Itself," (with R.J. Gardner),__Geometriae____Dedicata__, 26(1988), 323-331. - "Hausdorff Dimension in Graph Directed
Constructions," (with S. C. Williams), Transactions American
Mathematical Society, 309(1988), 811-829.
- "Mathematics
of dimension measurement for graphs of functions," (with P.
Carter and R. Cawley), in
__Fractal Aspects of Materials: Disordered Systems__, edited by D. A. Weitz, L. M. Sander and B. B. Mandelbrot, Materials Research Society, Pittsburg, 1988,183-186. - "Rigorous
multifractal analysis,"(with R. Cawley and S. Hamel), in
__Fractal Aspects of Materials: Disordered Systems__, edited by D. A. Weitz, L. M. Sander and B. B. Mandelbrot, Materials Research Society, Pittsburg, 1988, 131-134. - "Probability and Nonlinear
Systems,"
__Los Alamos Science__, No. 15, Fall l987, 52-90. Reprinted in__From Cardinals to Chaos__, Edited by Necia Grant Cooper, Cambridge University Press, 1989. - Editor,
*Measure and Measurable Dynamics*,__Contemporary Mathematics__, 94(1989), published by the American Mathematical Society, Providence, R. I., 349 pages. - "One-to-one
selections and orthogonal transition kernels,"
*Measure and Measurable Dynamics*,__Contemporary Mathematics__, 94(1989), 185-190. - "A
classification of disintegrations of measures," (with S.Graf),
*Measure and Measurable Dynamics*,__Contemporary Mathematics__, 94(1989), 147-158. - "Scaling
Hausdorff measures," (with S. C.
Williams),
__Mathematika__, 36(1989), 325-333. - "Borel measurable selections and applications of the boundedness principle," (with G. Schlee),
__Real Analysis Exchange__, 15(1) (1989), 70-92.

*1990-1999*

- "Reinforced
random walks and random distributions,"(with S. C. Williams),
Proceedings of the American Mathematical Society, 110 (1990), 251-258.
- "The
Birkhoff center and analytic sets,"
American Journal of Mathematics, 112(1990), 97-105.
- "Problems
in topology arising from analysis," in
__Open Problems in Topology__, edited by J. V. Mill and G. M. Reed, North Holland Publishing Co., Amsterdam, 1990, 619-629. - "Some
orthogonality preserving kernels which are not
completely orthogonal," (with H.v.
Weizsacker), Annals of Probability, 19(1)
(1991), 396-400.
- "Non-uniformization results for the projective
hierarchy" (with Steve Jackson), Journal of Symbolic Logic, 56(1991),
742-748.
- "Polya trees and random distributions," (with W.
D. Sudderth and S. C. Williams), Annals of
Statistics, 20(1992), 1203-1221.
- "Multifractal decompositions of Moran fractals,"
(with R. Cawley),
__Advances in Mathematics__, 92(1992), 196-236. - "Continua
with [sigma]-finite linear measure," in Measure Theory, Oberwolfach 1990, Proceedings of the Conference held
at Oberwolfach, March 18-24, 1990
__Supplemento____di Rendiconti del Circolo Matematico di Palermo__, serie II, no. 38, 1992. - "Some
complexity results in topology and analysis," (with S. Jackson),
__Fundamenta____Mathematicae__, 141(1992), 75-83. - "Multifractal decompositions of digraph recursive
fractals," (with G.A.Edgar),
__Proceedings London Mathematical Society__, 65(1992), 604 -628. - "Random
circle homeomorphisms," (with T. Downarowicz
and T. Warnock),
__Ergodic____Theory and Dynamical Systems,__12(1992), 441-458. - "Borel measurable selections of Paretian
utility functions," (with S. Jackson),
__Journal of Mathematical Economics__, 23(1994), 361-378. - "Conformal
repellors with topological dimension one are
Jordan curves," (with M. Urbanski),
__Pacific Journal of Mathematics__, 166(1994), 83-96. - "On
partitions of lines and planes," (with P. Erdos
and S. Jackson),
__Fundamenta____Mathematicae__, 145(1994), 101-119. - "Randomly
generated distributions," (with M. Monticino),
Israel Journal of Mathematics, 91(1995), 91-110.
- "Infinite
iterated function systems: Theory and applications," in
__Fractal Geometry and Stochastics Progress in Probability__37, 1995, edited by C. Bandt, S. Graf, and M. Zahle, Birkhauser, Basel. - "Directionally
reinforced random walks," (with M. Monticino
and H.v. Weiszacker),
__Advances in Mathematics__, 117(1996), 239-252. - "Analytic non-Borel sets modulo null sets," Proceedings of the
BEST Conferences 1-3, Boise, Idaho, Edited by T. Bartoszynski
and M. Scheepers,
__Contemporary Mathematics__, 192(1996), 69-70. - "Dimensions
and measures in infinite iterated function systems, (with M. Urbanski),
__Proceedings London Mathematical Society__,73(1996), 105-154.

- "The
order type of the set of Pisot numbers," (with
David W. Boyd),
__Topology and Its Applications__, 69(1996), 115-120. - "Redistribution
of Velocity: Collision Transformations" (with S. C. Williams), in
__Statistics, Probability and Game Theory, Papers in Honor of David Blackwell__, Institute of Mathematical Statistics, Lecture Notes - Monograph Series 30, 1996, 21 pages. - "Measure
and dimension functions: Measurability and densities," (with P. Mattila),
__Proc. Cambridge Phil. Soc.__, 121(1997), 81-100. - "Generic
properties of open billiards," (with A. Lopes),
__J. Math Anal. Appl.__, 205(1997), 251-258. - "On
infinite partitions of lines and space" (with P. Erdos and S. Jackson),
__Fundamenta____Mathematicae__, 152(1997), 75-95. A generalization of Fermat's last theorem: the Beal Conjecture and Prize Problem, Notices American Mathematical Society, 44 (1997), 1436-1437. - "On
sets which meet each line in exactly two points,"
__Bull. London Math. Soc. ,__30(1998), 397-403. propties of sets defined by restrictions on thier exapansions in various bases - the see paper by Mauldin and williams in the TAMS - "The
equivalence of some Bernoulli convolutions to Lebesgue
measure" (with K. Simon),
__Proc. Amer. Math. Soc.__, 126(1998), 2733-2736. - "On
the uniqueness of the density for the invariant measure in an infinite
hyperbolic iterated function system" (with M. Urbanski),
__Periodica____Mathematica Hungarica__, Vol. 37 (1-3), (1998), 47-53. - "Conformal
measures for rational functions revisited" (with M. Denker, Z. Nitecki and M. Urbanski),
__Fund. Math.__, 157(1998), 161-173. - "Dimension
and measures for a curvilinear Sierpinski gasket
or Apollonian packings " (with M. Urbanski),
__Advances in Mathematics__, 136(1998), 26-38. - "Conformal
iterated function systems with applications to the geometry of continued
fractions" (with M. Urbanski),
__Trans. Amer. Math. Soc.__, 351(1999), 4995-5025. - "On
the sigma-class generated by open balls " (with
S. Jackson),
__Proc. Cambridge Phil. Soc.__, 127 (1999), 99-108. - "Sur
les series de translatees de fonctions
positives" (with Z. Buczolich and J.-P.
Kahane), C.R. Acad. Sci. Paris, t. 329, Serie I, (1999), 261-264. Erratum
C.R. Acad. Sci. Paris, t. 329. Serie I, p. 855,
1999.
- "On
the convergence of series of translates for
measurable functions," (with Z. Buczolich),
__Mathematika__,46 (1999), 337-341.

*2000-*

- "Parabolic
iterated function systems"(with M. Urbanski),
__Ergodic____Theory and Dynamical Systems__, 20 (2000), 1423-1447. - "Random
linear cellular automata: Fractals associated with random multiplication of
polynomials," (with G. Skordev),
__Japanese J. Math.__, 26 (2000), 381-406. - "No
n point set is sigma Compact," (with K. Bouhjar
and J. J. Dijkstra),
__Proc. Amer. Math. Soc.__, 129 (2000), 621-622. - "Rigidity
of conformal iterated function systems" (with F. Przytycki and M. Urbanski),
__Compositio____Math.,__129 (2001), 273-299. - "On
series of translates of positive functions," (with Z. Buczolich and J. Kahane),
__Acta____Mathematica Hungarica,__98 (2001), 171-188. - "Scaling
properties of Hausdorff and packing
measures," (with M. Csornyei),
__Math. Ann.,__319 (2001), 817-836. - "Rigidity
of connected limit sets of conformal IFS," (with V. Mayer and M. Urbanski),
__Mich. Math. J. ,__. 49 (2001), 451-458. - "Thermodynamic
formalism and multifractal analysis of conformal
infinite iterated function systems" (with P. Hanus
and M. Urbanski),
__Acta____Mathematica Hungarica,__96 (2002), 27-98. - "Deterministic
and Random aspects of porosities," (with E. and M. Jarvenpaa),
__Discrete and Continuous Dynamics,__8 (2002), 121-136. - "Fractal
measures for parabolic IFS," (with M. Urbanski),
__Advances Math.__, 168 (2002), 225-253. - "Gibbs
states on the symbolic space over an infinite alphabet," (with M.
Urbanski),
__Israel J. Math.__, 125 (2001), 93-130. - "Packing
measure and dimension of random fractals," (with A. Berlinkov),
__Journal of Theoretical Probability ,__15 (2002), 695-713. - "Fubini-type theorems for general measure
constructions," (with K.J. Falconer),
__Mathematika__, 47 (2000), 251-265. - "On
a lattice problem of H. Steinhaus," (with
S. Jackson),
__Journal Amer. Math. Soc.__15 (2002), 817-856. - "Some
problems in set theory, geometry and analysis," in Paul Erdos and his Mathematics I; editors: G. Halasz, L. Lovasz, M. Simonovits and V. T. Sos., Bolyai Society Mathematical Studies,
Volume I, pages 493-505, 2002.
- "On
series of translates of positive functions II," (with Z. Buczolich),
__Indagationes____Mathematicae__, 12 (2001), 317-327. - "Quantization
dimension for conformal iterated function systems," (with L.
Lindsay),
__Nonlinearity__, 15 (2002), 189-199. - "Some
comments on infinite Boolean functions," (with U. Darji and C. Freiling),
__Colloquium Mathematicum__, 94 (2002), 235-241. - "The
doubling property of conformal measures of infinite iterated function
systems," (with M. Urbanski), J. Number
Th. 102 (2003), 23-40.
- "Comments
on the Steinhaus tiling problem," (with
A. Yingst), Proc. Amer. Math. Soc., 131 (2003),
2071-2079.
- "Sets
meeting isometric copies of the lattice Z^2 in exactly one point," (with
S. Jackson), Proc. Nat'l Acad. Sci., 99
(25), (2002), 15883-15887.
- "Graph Directed Markov Systems:
Geometry and Dynamics of Limit Sets,"
(with M. Urbanski), Cambridge Tracts in
Mathematics, 148, Cambridge University Press, 2003.
- "Ergodic optimization for non-compact dynamical
systems," (with O. Jenkinson and M. Urbanski), Dynamical Systems, 22 (2007),
379-388 .
- "Survey
of the Steinhaus tiling problem,"(with
S. Jackson), Bull. Symbolic Logic, 9
(2003), 335-361.
- "Counting
and convergence in ergodic theory,"(with
I. Assani and Z. Buczolich),
Acta Univ. Carolinae,
45 (2004), 5-21.
- "An L^1
counting problem in ergodic theory,"(with
I.Assani and Z. Buczolich),
J. d' Analyse Math., 95 (2005), 221-241.
- "Some remarks
about output measures,"(with T. Downarowicz),
__Topology and Its Applications,__152 (2005), 11-25. - "Zero
temperature limits of Gibbs-equilibrium states for countable alphabet subshifts of finite type," (with O. Jenkinson and M. Urbanski),
J. Stat. Physics, 119 (2005), 765-776.
- "On homeomorphic Bernoulli measures on the Cantor
space," ( with R. Dougherty and A. Yingst), Trans. Amer. Math. Soc., 359 (2007),
6155-6166.
- "On the
unique representation of families of sets," (with S. Gao, S. Jackson and M. Laczkovich), Trans. Amer. Math. Soc., 20 360 (2008), 939-958.
- "Ergodic optimization for countable alphabet subshifts of finite type," (with O. Jenkinson and M. Urbanski ), Ergodic Theory and
Dynamics Systems, 26 (2006), 1791-1803.
- " Steinhaus tiling
problem and integral quadratic forms," (with W.K Chan),
Proc. Amer. Math. Soc., 135 (2007), 337-342.
- "Concepts
behind divergent ergodic averages along
squares," (with Z. Buczolich), Contemp.
Math., 430 , Amer. Math. Soc., Providence, RI,
2007 22 pages.
- "Which
Bernoulli measures are good," (with E. Akin, R. Dougherty and A. Yingst), Colloquium Mathematicum,
110 (2008), 243-291.
- "Constructing 1-M families, " the base case for the induction argument
of divergent square averages., with Z. Buczolich,
unpublished manuscript.
- "A polynomial fixed point
theorem," (with P. Allaart),
Real Analysis Exchange 33 (2008), 495-496.
- "Injectivity of the Dubins-Freedman
construction of random distributions," (with P. Allaart), Contemp. Math. 485 (2009), 1-6
- "Homeomorphic Bernoulli measures and ergodic theory," (with A. Yingst), Contemp. Math., 485 (2009), 131-142.
- ."Random
closed sets viewed as random recursions," (with A. McLinden), Arch. Math. Logic 48 (2009), 257-263.
- "Graph
directed Markov systems on Hilbert spaces," (with T. Szarek and M. Urbanski), Math. Proc. Cambridge Phil. Soc. 147
(2009), 455-488.
- "Divergent Square Averages," (with Z. Buczolich), Ann. Math., 171 (2010), 1479-1530.
- "Translating the Cantor set by a random real,"(with R. Dougherty, J. H. Lutz and J. Teutsch), 152, (2014),
- "On the Steinhaus
tiling problem in three dimensions," (with D. Goldstein), Quarterly J.
Math., to appear.
- "The motif problem," (with E.
R. Canfield, R. Fertig, and D. Moews), preprint
- "Some problems and ideas of Erdos in analysis and geometry," Erdos Centennial Bolyai Society Mathematical Studies, Vol. 25, Springer, 2013.
- "Bijective proofs of Jensen's and Mohanty-Handa's identities," (with N. A. Loehr), Applicable Analysis and Discrete Mathematics, 7 (2013), 11-24.