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Borel spaces

100%

Rao K. P. S. B., Rao B. V.

Instytut Matematyczny Polskiej Akademii Nauk

EN

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

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Completeness of $L_1$ spaces over finitely additive probabilities

92%

Gangopadhyay S., Rao B. V.

Colloquium Mathematicum

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1999

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tom 80

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nr 1

83-95

3

Mixtures of non-atomic measures, II

55%

Bhaskara Rao K. P. S., Rao B. V.

Colloquium Mathematicum

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1975

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tom 33

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nr 1

105-112

4

Mixtures of nonatomic measures. III

55%

Bhaskara Rao K. P. S., Rao B. V.

Colloquium Mathematicum

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1979

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tom 41

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nr 1

85-88

5

Remarks on generalized analytic sets and the axiom of determinateness

55%

Rao B. V.

Fundamenta Mathematicae

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1970

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tom 69

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nr 2

125-129

6

On extensions of measures

46%

Bhaskara Rao K. P. S., Rao B. V.

Colloquium Mathematicum

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1987

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tom 53

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nr 1

43-47

7

Generalizations of Castaing's theorem on selectors

46%

Maitra A., Rao B. V.

Colloquium Mathematicum

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1979

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tom 42

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nr 1

295-300

8

Selection theorems for partitions of Polish spaces

46%

Maitra A., Rao B. V.

Fundamenta Mathematicae

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1976

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tom 93

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nr 1

47-56

9

Non-existence of certain Borel structures

46%

Rao B. V.

Fundamenta Mathematicae

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1970

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tom 69

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nr 3

241-242

10

Remarks on vector sums of Borel sets

46%

Rao B. V.

Colloquium Mathematicum

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1972

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tom 25

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nr 1

103-104

11

Borel structures for function spaces

46%

Rao B. V.

Colloquium Mathematicum

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1971

|

tom 23

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nr 1

33-38

12

On Borel structures

37%

Rao B. V.

Colloquium Mathematicum

|

1970

|

tom 21

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nr 2

199-204

13

Remarks on analytic sets

37%

Rao B. V.

Fundamenta Mathematicae

|

1970

|

tom 66

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nr 2

237-239

14

Lattice of Borel structures

37%

Rao B. V.

Colloquium Mathematicum

|

1971

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tom 23

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nr 2

213-216

Ograniczanie wyników

9 Colloquium Mathematicum

4 Fundamenta Mathematicae

14 Rao B. V.

3 Bhaskara Rao K. P. S.

2 Maitra A.

1 Gangopadhyay S.

1 Rao K. P. S. B.

1 1999

1 1987

1 1981

2 1979

1 1976

1 1975

1 1972

2 1971

4 1970

Borel spaces

Completeness of $L_1$ spaces over finitely additive probabilities

Mixtures of non-atomic measures, II

Mixtures of nonatomic measures. III

Remarks on generalized analytic sets and the axiom of determinateness

On extensions of measures

Generalizations of Castaing's theorem on selectors

Selection theorems for partitions of Polish spaces

Non-existence of certain Borel structures

Remarks on vector sums of Borel sets

Borel structures for function spaces

On Borel structures

Remarks on analytic sets

Lattice of Borel structures