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Pettis integral and measure theory

Author: Michel Talagrand
Publisher: Providence, R.I. : American Mathematical Society, ©1984.
Series: Memoirs of the American Mathematical Society, no. 307.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
We present a self-contained account of measure theory and integration in a Banach space. We give a detailed analysis of the weak Baire probabilities on a Banach space E, and on its second dual. Scalarly (= weak) measurable functions valued in E are studied via their image measure and it is shown how to regularize them using lifting. General criteria are given to ensure that they are Pettis integrable. This study  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Michel Talagrand
ISBN: 0821823078 9780821823071
OCLC Number: 10948902
Description: ix, 224 pages ; 26 cm.
Contents: Measure theory prerequisites --
Measurability in a Banach space --
Scalarly measurable functions --
The Dunford and Pettis integrals --
Criteria for Pettis integrability --
Properly measurable functions --
The weak RNP and related properties --
Fremlin's subsequence theorem --
Basic lemma --
Joint measurability --
Convex hull and conditional expectation --
On a problem of A. Bellow --
Filters and extension of measure --
Pointwise compacts of Baire-measurable functions --
Translations in groups --
Further topics on measurability in a Banach space.
Series Title: Memoirs of the American Mathematical Society, no. 307.
Responsibility: Michel Talagrand.

Abstract:

We present a self-contained account of measure theory and integration in a Banach space. We give a detailed analysis of the weak Baire probabilities on a Banach space E, and on its second dual. Scalarly (= weak) measurable functions valued in E are studied via their image measure and it is shown how to regularize them using lifting. General criteria are given to ensure that they are Pettis integrable. This study relies on tools from topological and abstract measure theory.

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