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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction......................................................................................5
1. Blackwell spaces..........................................................................5
1.1. Blackwell spaces without the strong Blackwell property...........6
1.2. Blackwell properties and density..............................................8
1.3. Sierpiński sets and the Blackwell property.............................18
1.4. Products and intersections of Blackwell sets.........................22
2. Lattice of subalgebras...............................................................24
2.1. Complements........................................................................25
2.2. Maximal conjugates...............................................................26
2.3. Minimal complements............................................................33
3. Further topics............................................................................37
3.1. Generators and minimal generators......................................37
3.2. Rigid and strongly rigid Borel spaces....................................40
3.3. The extension property.........................................................42
Appendix I.....................................................................................45
Appendix II....................................................................................46
References...................................................................................47
Introduction......................................................................................5
1. Blackwell spaces..........................................................................5
1.1. Blackwell spaces without the strong Blackwell property...........6
1.2. Blackwell properties and density..............................................8
1.3. Sierpiński sets and the Blackwell property.............................18
1.4. Products and intersections of Blackwell sets.........................22
2. Lattice of subalgebras...............................................................24
2.1. Complements........................................................................25
2.2. Maximal conjugates...............................................................26
2.3. Minimal complements............................................................33
3. Further topics............................................................................37
3.1. Generators and minimal generators......................................37
3.2. Rigid and strongly rigid Borel spaces....................................40
3.3. The extension property.........................................................42
Appendix I.....................................................................................45
Appendix II....................................................................................46
References...................................................................................47
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
372
Liczba stron
48
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLXXII
Daty
wydano
1997
otrzymano
1996-12-23
Twórcy
autor
- Wesleyan University, Middletown, Connecticut 06457, U.S.A.
autor
- Indian Statistical Institute, Bangalore 560059, India
Bibliografia
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- [3] B. Aniszczyk, A rigid Borel space, Proc. Amer. Math. Soc. 113 (1991), 1013-1015.
- [4] B. Aniszczyk and R. Frankiewicz, On minimal generators of σ-fields, Fund. Math. 124 (1984), 131-134.
- [5] J. Baumgartner, Letter to R. M. Shortt, June 25, 1986.
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- [18] N. Falkner, Generalizations of analytic and standard measurable spaces, Math. Scand. 49 (1981), 283-301.
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- [23] F. Hausdorff, Summen von ℵ₁ Mengen, Fund. Math. 26 (1936), 241-255.
- [24] J. Jasiński, On the combinatorial properties of Blackwell spaces, Proc. Amer. Math. Soc. 93 (1985), 657-660.
- [25] J. Jasiński, On the Blackwell property of Luzin sets, Proc. Amer. Math. Soc. 95 (1985), 303-306.
- [26] J. Jasiński, A solution to the problem of B. V. Rao on Borel structures, Colloq. Math. 54 (1987), 167-170.
- [27] T. J. Jech, Trees, J. Symbolic Logic 36 (1971), 1-14.
- [28] H. G. Kellerer, Duality theorems for marginal problems, Z. Wahrsch. Verw. Gebiete 67 (1984), 399-432.
- [29] K. Kuratowski, Topology, Vol. 1, Academic Press, 1966.
- [30] A. Maitra, Extensions of measurable functions, Colloq. Math. 44 (1981), 99-104.
- [31] R. D. Mauldin, Countably generated families, Proc. Amer. Math. Soc. 54 (1976), 291-297.
- [32] C. A. Rogers et al., Analytic Sets, Academic Press, London, 1980.
- [33] H. Sarbadhikari, A note on reticulated sets, note of 1985.
- [34] H. Sarbadhikari, A projective Blackwell space which is not analytic, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 21 (1973), 511-514.
- [35] R. M. Shortt, The extension of measurable functions, Proc. Amer. Math. Soc. 87 (1983), 444-446.
- [36] R. M. Shortt, Borel density, the marginal problem and isomorphism types of analytic sets, Pacific J. Math. 113 (1984), 183-200.
- [37] R. M. Shortt, Reticulated sets and the isomorphism of analytic powers, Pacific J. Math. 119 (1985), 215-226.
- [38] R. M. Shortt, Minimal complementation and maximal conjugation for partitions, with an application to Blackwell sets, Fund. Math. 34 (1984), 211-223.
- [39] R. M. Shortt, A separation principle for Blackwell sets, Bull. Polish Acad. Sci. Math. 34 (1986), 643-645.
- [40] R. M. Shortt, Sets with no uncountable Blackwell subsets, Czechoslovak Math. J. 37 (1986), 320-322.
- [41] R. M. Shortt, Borel-dense Blackwell spaces are strongly Blackwell, Colloq. Math. 53 (1987), 35-41.
- [42] R. M. Shortt, Combinatorial properties for Blackwell sets, Proc. Amer. Math. Soc. 101 (1987), 738-742.
- [43] R. M. Shortt, Maximally conjugate sigma-algebras represented as hypergraphs, Fund. Math. 130 (1988), 27-49.
- [44] R. M. Shortt, A criterion for measurability of countable-to-one functions, Real Anal. Exchange 4 (1988-89), 498-500.
- [45] R. M. Shortt, Measurable and topological rigidity, in: Ann. New York Acad. Sci. 552, New York Acad. Sci., 1989, 152-160.
- [46] R. M. Shortt, Measurable rigidity, super-rigidity and the Blackwell property, Indian J. Math. 31 (1989), 201-214.
- [47] R. M. Shortt and K. P. S. Bhasakara Rao, Generalized Lusin sets with the Blackwell property, Fund. Math. 127 (1986), 9-39.
- [48] R. M. Shortt and J. van Mill, Automorphism groups for measurable spaces, Topology Appl. 30 (1988), 27-42.
- [49] J. Steel, Analytic sets and Borel isomorphisms, Fund. Math. 108 (1980), 82-88.
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Języki publikacji
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Uwagi
1991 Mathematics Subject Classification: 28A05, 04A15, 03E15.
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0012-3862
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