Constructive measure theory
A general, constructive measure theory is given in terms of Daniell integrals as part of the systematic development of the constructive component of analysis. Integration spaces are first defined in terms of a linear function on the space of integrable functions on a basic set. The space of integrable functions is then extended by continuity. Integrable sets are defined, their properties proved. A theory of profiles is introduced to prove the existence of (to construct) an abundance of integrab…
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- Full title :Constructive measure theory / by Errett Bishop and Henry Cheng.
Summary
A general, constructive measure theory is given in terms of Daniell integrals as part of the systematic development of the constructive component of analysis. Integration spaces are first defined in terms of a linear function on the space of integrable functions on a basic set. The space of integrable functions is then extended by continuity. Integrable sets are defined, their properties proved. A theory of profiles is introduced to prove the existence of (to construct) an abundance of integrable sets. The usual convergence theorems are proved. The more common measure space approach is then dealt with and shown to be equivalent to the integration space approach taken. Product measures are constructed and Fubini's theorem proved, and the approach taken by the authors is elegant and general. Constructive proofs are immediately linked to computations.
Read More ↓Edition Statements
- Publication Date:©1972.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, R.I
- Language:eng
- Publication Date:©1972.
The Physical Object
- Description:v, 85 pages ; : 25 cm.
Edition Identifiers
- ISBN:0821818163, 9780821818169
- oclc:ocm00314804
- LC Classification:QA3
- Dewey Decimal:515/.42
Table of Contents
Integration spaces -- Integrable sets -- The theory of profiles -- Measurable functions and the convergence of integrals -- Measure for measure -- Product measures and Fubini's theorem -- Approximation by compact sets in a locally compact integration space.
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