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Pettis integral and measure theory

About this Title

Michel Talagrand

Publication: Memoirs of the American Mathematical Society
Publication Year 1984: Volume 51, Number 307
ISBNs: 978-0-8218-2307-1 (print); 978-1-4704-0720-9 (online)
MathSciNet review: 756174
MSC: Primary 46G10; Secondary 28B05, 46B20

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Table of Contents


  • 1. Measure theory prerequisites
  • 2. Measurability in a Banach space
  • 3. Scalarly measurable functions
  • 4. The Dunford and Pettis integrals
  • 5. Criteria for Pettis integrability
  • 6. Properly measurable functions
  • 7. The weak RNP and related properties
  • 8. Fremlin’s subsequence theorem
  • 9. Basic lemma
  • 10. Joint measurability
  • 11. Convex hull and conditional expectation
  • 12. On a problem of A. Bellow
  • 13. Filters and extension of measure
  • 14. Pointwise compacts of Baire-measurable functions
  • 15. Translations in groups
  • 16. Further topics on measurability in a Banach space