Borel spaces

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

GDML_Books, (1981), p.

Résumé

CONTENTSIntroduction............................................................................... 5Chapter 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..................................................... 20Chapter 2. Blackwell spaces................................................ 21 § 8. Blackwell spaces............................................... 21 § 9. Nonanalytic Blackwell spaces................................. 24 § 10. Coanalytic Blackwell spaces................................. 26 § 11. Combinatorial properties........................................ 27Chapter 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........................ 40Chapter 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............................................ 58References............................................................................... 60Index to problems................................................................... 63

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