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Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction............................................................................... 5
Chapter 1. Borel spaces........................................................ 7
§ 1. Borel spaces....................................................... 7
§ 2. Classical descriptive set theory............................... 10
§ 3. Measure and category............................................... 12
§ 4. Countably generated structures.............................. 13
§ 5. Product spaces........................................................... 17
§ 6. Minimal generators.................................................... 19
§ 7. Rigid Borel spaces..................................................... 20
Chapter 2. Blackwell spaces................................................ 21
§ 8. Blackwell spaces............................................... 21
§ 9. Nonanalytic Blackwell spaces................................. 24
§ 10. Coanalytic Blackwell spaces................................. 26
§ 11. Combinatorial properties........................................ 27
Chapter 3. Atomless structures........................................... 29
§ 12. Atomless structures........................................ 29
§ 13. Atomless substructures of given structures....... 31
§ 14. Separated atomless structures............................. 35
§ 15. Combinatorial properties........................................ 36
§ 16. Measures on atomless structures........................ 40
Chapter 4. Lattice of Borel structures.................................. 41
§ 17. Lattice of Borel structures....................................... 41
§ 18. Atoms and antiatoms.............................................. 42
§ 19. Complementation.................................................... 45
§ 20. A sublattice of $L_X$............................................... 54
§ 21. Embedding................................................................ 56
§ 22. Power of $L_X$......................................................... 56
§ 23. Isomorphism problem............................................ 58
References............................................................................... 60
Index to problems................................................................... 63
Introduction............................................................................... 5
Chapter 1. Borel spaces........................................................ 7
§ 1. Borel spaces....................................................... 7
§ 2. Classical descriptive set theory............................... 10
§ 3. Measure and category............................................... 12
§ 4. Countably generated structures.............................. 13
§ 5. Product spaces........................................................... 17
§ 6. Minimal generators.................................................... 19
§ 7. Rigid Borel spaces..................................................... 20
Chapter 2. Blackwell spaces................................................ 21
§ 8. Blackwell spaces............................................... 21
§ 9. Nonanalytic Blackwell spaces................................. 24
§ 10. Coanalytic Blackwell spaces................................. 26
§ 11. Combinatorial properties........................................ 27
Chapter 3. Atomless structures........................................... 29
§ 12. Atomless structures........................................ 29
§ 13. Atomless substructures of given structures....... 31
§ 14. Separated atomless structures............................. 35
§ 15. Combinatorial properties........................................ 36
§ 16. Measures on atomless structures........................ 40
Chapter 4. Lattice of Borel structures.................................. 41
§ 17. Lattice of Borel structures....................................... 41
§ 18. Atoms and antiatoms.............................................. 42
§ 19. Complementation.................................................... 45
§ 20. A sublattice of $L_X$............................................... 54
§ 21. Embedding................................................................ 56
§ 22. Power of $L_X$......................................................... 56
§ 23. Isomorphism problem............................................ 58
References............................................................................... 60
Index to problems................................................................... 63
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
190
Liczba stron
62
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CXC
Daty
wydano
1981
Twórcy
autor
autor
Bibliografia
- [1] R. J. Aumann, BoreI structures for function spaces, Ill. J. Math. 5 (1961), 614-630.
- [2] D. Basu, Problems relating to the existence of maximal and minimal elements in some fields of statistics (subfields), Proc. fifth Berkeley Symp., Vol. 1 (1965), 41-50.
- [3] K. P. S. Bhaskara Rao, Studies in Boolean algebras and measure theory, thesis, Indian Statistical Institute, Calcutta 1972.
- [4] K. P. S. Bhaskara Rao and B. V. Rao, On the isomorphism problem for analytic sets, Bull. Acad. Polon. Sci. 26 (1978), 767-769.
- [5] K. P. S. Bhaskara Rao and B. V. Rao, Mixtures of nonatomic measures, II, Colloq. Math. 33 (1975), 105-112.
- [6] K. P. S. Bhaskara Rao and B. V. Rao, Atomless structures and σ-independence. Bull. Acad. Polon. Sci. 26 (1978), 783-784.
- [7] K. P. S. Bhaskara Rao and B. V. Rao, Lattice of Borel structures, ibid. 26 (1978), 785-786.
- [8] K. P. S. Bhaskara Rao and M. Bhaskara Rao, A note on the countable chain condition and a finiteness of measures, Bull. Aust. Math. Soc. 6 (1972), 349-353.
- [9] K. P. S. Bhaskara Rao and M. Bhaskara Rao, A remark on nonatomic measures, Ann. Math. Stat. 43 (1972), 369-370.
- [10] M. Bhaskara Rao and K. P. S. Bhaskara Rao, Borel σ-algebra on [0,Ω], Manuscripta Math. 5 (1971), 195-198.
- [11] M. Bhaskara Rao and K. P. S. Bhaskara Rao, Cardinalities of Banach spaces, Journ. Indian Math. Soc. 37 (1973), 347-349.
- [12] G. Birkhoff, Lattice theory, Amer. Math. Soc., Coll. pub., Vol. 25 (1967).
- [13] D. Blackwell, On a class of probability spaces, Proc. third. Berkeley Symp., Vol. 2 (1954), 1-6.
- [14] D. Blackwell and L. E. Dubins, On existence and nonexistence of proper, regular, conditional distributions, Ann. Prob. 3 (1975), 741-752.
- [15] J. de Groot, Groups represented by homeomorphism groups I, Math. Ann. 138 (1959), 80-102.
- [16] G. Fichtenholz and L. Kantorovitch, Sur les opérations linéaires dans l'espaces des fonctions bornées, Studia Math. 5 (1934), 69-98.
- [17] Z. Frolik, Stone-Weierstrass theorems for C(X) with the sequential topology, Proc. Amer. Math. Soc. 27 (1971), 486-494.
- [18] G. Grätzer, Universal algebra, D. Van Nostrand Inc., Princeton 1968.
- [19] P. R. Halmos, Measure theory, D. Van Nostrand Co., New York 1950.
- [20] L. Harrington, Analytic determinancy and $0^H$, preprint, 1977.
- [21] F. Hausdorff, Set theory, 2nd ed., Chelsea, New York 1962.
- [22] J. Hoffman-Jørgensen, The theory of analytic spaces, Various publications series. No. 10, Aarhus University, 1970.
- [23] B. Jónsson, A Boolean algebra without proper automorphisms, Proc. Amer. Math. Soc. 2 (1951), 766-770.
- [24] S. Kakutani and J. C. Oxtoby, Construction of a nonseparable invariant extension of the Lebesgue measure space, Ann. Math. 52 (1950), 580-590.
- [25] M. Katětov, Remarks on Boolean algebras, Colloq. Math. 2 (1951), 229-235.
- [26] M. Kondo, Sur la représentation paramétrique régulière des ensembles analytiques, Fund. Math. 31 (1938), 29-46.
- [27] K. Kunen, Inaccessibility properties of cardinals, thesis, Stanford University, Stanford 1968.
- [28] K. Kuratowski, Topology, I. Academic Press-PWN. New York - Warszawa 1966.
- [29] K. Kuratowski and A. Mostowski, Set theory, 2nd ed., North-Holland, Amsterdam 1976.
- [30] R. E. Larson and S. J. Andima, The lattice of topologies: a survey, Rocky, Mountain J. Math. 5 (1975), 177-197.
- [31] N. Lusin, Leçon sur les ensembles analytiques, Gauthier-Villars, Paris 1930.
- [32] G. W. Mackey, Borel structures in groups and their duals, Trans. Amer. Math. Soc. 85 (1957), 134-165.
- [33] A. Maitra, Coanalytic sets that are not Blackwell spaces, Fund. Math. 67 (1970), 251-254.
- [34] A. Maitra, B. V. Rao and K. P. S. Bhaskara Rao, A problem in the extension of measures, Ill. J. Math. 23 (1979), 211-216.
- [35] R. Mansfield, The solution to one of Ulam's problems concerning analytic rectangles, Proc. Summer institute on set theory, UCLA, Los Angeles, 1967, 241-245.
- [36] R. Mansfield, The solution to one of Ulam's problems concerning analytic sets, II, Proc. Amer. Math. Soc. 26 (1970), 539-540.
- [37] E. Marczewski, The characteristic function of a sequence of sets and some of its applications, Fund. Math. 31 (1938), 207-223.
- [38] E. Marczewski, Ensembles indépendants et leurs applications à la théorie de la mesure, ibid. 35 (1948), 13-28.
- [39] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), 143-178.
- [40] P. A. Meyer, Probability and potentials, Blaisdell Publishing Company, Boston 1966.
- [41] P. S. Novikov, Sur les fonctions implicites mesurables B, Fund. Math. 17 (1931), 8-25.
- [42] M. Orkin, A Blackwell space which is not analytic, Bull. Acad. Polon. Sci. 20 (1972), 437-438.
- [43] J. C. Oxtoby, Measure and category, Springer-Verlag, New York 1971.
- [44] D. Ramachandran, On the two definitions of independence, Colloq. Math. 32 (1975), 227-231.
- [45] B. V. Rao, Studies in Borel structures, thesis, Indian Statistical Institute, Calcutta 1969.
- [46] B. V. Rao, On discrete Borel spaces and projective sets, Bull. Amer. Math. Soc. 75 (1969), 614-617.
- [47] B. V. Rao, Nonexistence of certain Borel structures, Fund Math, 69 (1970), 241-242.
- [48] B. V. Rao, Remarks on analytic sets, ibid. 66 (1970), 237-239.
- [49] B. V. Rao, On Borel structures, Colloq. Math. 21 (1970), 199-204.
- [50] B. V. Rao, Lattice of Borel structures, ibid. 23 (1971), 213-216.
- [51] B. V. Rao, On discrete Borel spaces, Acta Math, Acad. Sci. Hung. 22 (1971), 197-198.
- [52] S. B. Rao, On the minimal thick sets of a measure space, Indian Journ. Math. 12 (1970), 31-41.
- [53] W. Rudin, Fourier analysis on groups. Interscience, New York 1967.
- [54] S. Saks, Theory of the integral, 2 nd ed., Dover, New York 1964.
- [55] H. Sarbadhikari, A projective Blackwell space which is not analytic, Bull. Acad. Polon. Sci. 21 (1973), 511-514.
- [56] H. Sarbadhikari, Some contributions to descriptive set theory, thesis, Indian Statistical Institute, Calcutta, 1977.
- [57] H. Sarbadhikari, K. P. S. Bhaskara Rao and E. Grzegorek, Complementation in the lattice of Borel structures, Colloq. Math. 31 (1974), 29-32.
- [58] W. Sierpiński, Sur un ensemble non dénombrable dont tout homeomorphe est de mesure nulle, Fund. Math. 7 (1925), 188-190.
- [59] W. Sierpiński, Les ensembles projectifs et analytiques, Gauthier-Villars, Paris 1950.
- [60] W. Sierpiński, L'hypothèse du continu, 2 nd éd., Chelsea, New York 1956.
- [61] R. M. Solovay, A model of set theory in which every set of reals is Lebesgue measurable, Ann. Math. 92 (1970), 1-56.
- [62] J. Steel. Ph. D. Thesis, University of California, Berkeley, 1976.
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