A Course on Borel Sets

Cardinal and Ordinal Numbers.- Topological Preliminaries.- Standard Borel Spaces.- Analytic and Coanalytic Sets.- Selection and Uniformization Theorems.

[1]  G. Choquet Theory of capacities , 1954 .

[2]  John von Neumann,et al.  Rings of operators , 1961 .

[3]  Alexander S. Kechris,et al.  The Descriptive Set Theory of Polish Group Actions: DESCRIPTIVE SET THEORY , 1996 .

[4]  John P. Burgess,et al.  Nonexistence of measurable optimal selections , 1992 .

[5]  D. Blackwell On a Class of Probability Spaces , 1956 .

[6]  A. Kechris Measure and category in effective descriptive set theory , 1973 .

[7]  Manfred SchÄl,et al.  Conditions for optimality in dynamic programming and for the limit of n-stage optimal policies to be optimal , 1975 .

[8]  Stephen G. Simpson,et al.  On the Existence of Two Analytic Non-Borel Sets Which are not Isomorphic , 1984 .

[9]  Gabriel Mokobodzki Demonstration elementaire d'un theoreme de Novikov , 1976 .

[10]  C. Dellacherie,et al.  Capacities and analytic sets , 2020, Large Cardinals, Determinacy and Other Topics.

[11]  John P. Burgess A selection theorem for group actions. , 1979 .

[12]  W. Arveson An Invitation To C*-Algebras , 1976 .

[13]  Alain Louveau,et al.  A Glimm-Effros dichotomy for Borel equivalence relations , 1990 .

[14]  D. Blackwell Discounted Dynamic Programming , 1965 .

[15]  H. Sarbadhikari,et al.  Random theorems in topology , 1990 .

[16]  H. Sarbadhikari,et al.  Complementation in the lattice of Borel structures , 1974 .

[17]  K. Gödel The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis. , 1938, Proceedings of the National Academy of Sciences of the United States of America.

[18]  L. Pukanszky,et al.  Unitary representations of solvable Lie groups , 1971 .

[19]  John R. Steel,et al.  On Vaught's conjecture , 1978 .

[20]  J. Dixmier Dual et quasi-dual d’une algèbre de Banach involutive , 1962 .

[21]  A. Maitra,et al.  Generalizations of Castaing's theorem on selectors , 1979 .

[22]  R. Baire Sur les fonctions de variables réelles , 1899 .

[23]  Maurice Sion On capacitability and measurability , 1963 .

[24]  K. Gödel Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I , 1931 .

[25]  Jon K. Cole A selector theorem in Banach spaces , 1971 .

[26]  A. H. Stone Non-separable Borel sets , 1962 .

[27]  M. Nadkarni Basic ergodic theory , 1995 .

[28]  Louis Auslander,et al.  Polarization and unitary representations of solvable Lie groups , 1971 .

[29]  G. Mackey Borel structure in groups and their duals , 1957 .

[30]  H. Lebesgue Sur les fonctions representables analytiquement , 1905 .

[31]  H. Sarbadhikari,et al.  Parametrizations of G δ -Valued Multifunctions , 1980 .

[32]  David Preiss The convex generation of convex Borel sets in Banach spaces , 1973 .

[33]  A. F. Filippov On Certain Questions in the Theory of Optimal Control , 1962 .

[34]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[35]  G. Mackey The theory of unitary group representations , 1976 .

[36]  Sławomir Solecki,et al.  Automatic continuity of group operations , 1997 .

[37]  H. Sarbadhikari A note on some properties of $A$-functions , 1976 .

[38]  L. J. Savage,et al.  Inequalities for Stochastic Processes: How to Gamble If You Must , 1976 .

[39]  John P. Burgess,et al.  Remarks on invariant descriptive set theory , 1975 .

[40]  C. Luther,et al.  INDEPENDENCE OF THE CONTINUUM HYPOTHESIS , 2009 .

[41]  Edward G. Effros,et al.  Transformation Groups and C ∗ -algebras , 1965 .

[42]  Haim Judah,et al.  Set Theory: On the Structure of the Real Line , 1995 .

[43]  Robert R. Kallman,et al.  A cross section theorem and an application to $C\sp*$-algebras , 1978 .

[44]  Daniel Lascar Why Some People are Excited by Vaught's Conjecture , 1985, J. Symb. Log..

[45]  Galen Weitkamp,et al.  Recursive Aspects of Descriptive Set Theory , 1985 .

[46]  É. Borel,et al.  Sur la classification des ensembles de mesure nulle , 1919 .

[47]  D. Blackwell,et al.  Infinite games and analytic sets. , 1967, Proceedings of the National Academy of Sciences of the United States of America.

[48]  P. Meyer,et al.  Probabilities and potential C , 1978 .

[49]  E. Michael Continuous Selections. I , 1956 .

[50]  Wacław Sierpiński,et al.  Sur la puissance des ensembles mesurables (B) , 1924 .

[51]  R. Vaught Invariant sets in topology and logic , 1974 .

[52]  Rao,et al.  AN ELEMENTARY PROOF OF THE BOREL ISOMORPHISM THEOREM , 1994 .

[53]  S. Sakai,et al.  On Type I C ∗ -Algebras , 1967 .

[54]  Slawomir Solecki,et al.  Equivalence relations induced by actions of Polish groups , 1995 .

[55]  15 Measurable Utility and the Measurable Choice Theorem , 1969 .

[56]  D. Blackwell,et al.  Non-Existence of Everywhere Proper Conditional Distributions , 1963 .

[57]  Irving Kaplansky,et al.  The structure of certain operator algebras , 1951 .

[58]  Alain Louveau,et al.  Descriptive Set Theory and the Structure of Sets of Uniqueness , 1987 .

[59]  Kenneth Kunen,et al.  Set Theory: An Introduction to Independence Proofs , 2010 .

[60]  James Glimm,et al.  Type I C ∗ -Algebras , 1961 .

[61]  H. Sarbadhikari Some uniformization results , 1977 .

[62]  J. Neumann On Rings of Operators. Reduction Theory , 1949 .

[63]  Alain Louveau,et al.  A separation theorem for Σ¹₁ sets , 1980 .

[64]  Motokiti Kondô Sur l'uniformisation des complémentaires analytiques et les ensembles projectifs de la seconde classe , 1939 .

[65]  R. Solovay A model of set-theory in which every set of reals is Lebesgue measurable* , 1970 .

[66]  J. Dixmier Les C*-algèbres et leurs représentations .. , 1964 .

[67]  A. C. Thompson,et al.  Theory of correspondences : including applications to mathematical economics , 1984 .

[68]  John P. Burgess A reflection phenomenon in descriptive set theory , 1979 .

[69]  B. V. Rao,et al.  ON DISCRETE BOREL SPACES AND PROJECTIVE SETS , 2007 .

[70]  J. Doob Classical potential theory and its probabilistic counterpart , 1984 .

[71]  S. M. Srivastava Transfinite numbers , 1997 .

[72]  J. Burgess Equivalences generated by families of Borel sets , 1978 .

[73]  S. M. Srivastava,et al.  SELECTION THEOREMS AND INVARIANCE OF BOREL POINTCLASSES , 1986 .

[74]  Andrzhei︠a︡ Mostowski,et al.  Set theory : with an introduction to descriptive set theory , 1976 .

[75]  Jacques Stern,et al.  Effective partitions of the real line into Borel sets of bounded rank , 1980 .

[76]  S. M. Srivastava Selection theorems for _{}-valued multifunctions , 1979 .

[77]  J. Diestel Sequences and series in Banach spaces , 1984 .

[78]  M. Schäl A selection theorem for optimization problems , 1974 .

[79]  Ramez L. Sami,et al.  Polish group actions and the Vaught conjecture , 1994 .

[80]  Felix Bernstein,et al.  Zum Kontinuumproblem , 2022 .

[81]  A. Maitra,et al.  Selectors for Borel sets with large sections , 1983 .

[82]  C. Castaing,et al.  Convex analysis and measurable multifunctions , 1977 .

[83]  J. W. Addison,et al.  Separation principles in the hierarchies of classical and effective descriptive set theory , 1958 .

[84]  S. Ulam A collection of mathematical problems , 1960 .

[85]  W. Sudderth,et al.  Discrete Gambling and Stochastic Games , 1996 .

[86]  Douglas E. Miller A Selector for Equivalence Relations with G δ Orbits , 1978 .

[87]  Douglas E. Miller On the measurability of orbits in Borel actions , 1977 .

[88]  F. Stephan,et al.  Set theory , 2018, Mathematical Statistics with Applications in R.

[89]  Wacław Sierpiński,et al.  Sur une classe d'ensembles , 2022 .

[90]  D. Blackwell A Borel Set Not Containing a Graph , 1968 .

[91]  Pierre Novikoff,et al.  Sur les fonctions implicites mesurables B , 1931 .

[92]  R. Vaught,et al.  Denumerable Models of Complete Theories , 1970 .

[93]  J. Silver,et al.  Counting the number of equivalence classes of Borel and coanalytic equivalence relations , 1980 .

[94]  C. J. Keyser Contributions to the Founding of the Theory of Transfinite Numbers , 1916 .

[95]  C. Castaing Sur les multi-applications mesurables , 1967 .

[96]  Paul Alexandroff Sur la puissance des ensembles mesurables B 162 , .

[97]  S. M. Srivastava A Representation Theorem for G δ -Valued Multifunctions , 1980 .

[98]  C. Kuratowski Sur une généralisation de la notion d'homéomorphie , 1934 .

[99]  Bapuji Rao Remarks on analytic sets , 1970 .

[100]  Jacques Stern,et al.  On Lusin's restricted continuum problem , 1984 .

[101]  C. Olech,et al.  Existence theorems for optimal problems with vector-valued cost function , 1969 .

[102]  James V. Bondar Borel Cross-Sections and Maximal Invariants , 1976 .