Essentials of Measure Theory
Classical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-semester beginning graduate course in measure theory, proposing an “abstract” approach to measure and integration, where the classical concrete cases of Lebesgue measure and Lebesgu...
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| Language: | English |
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Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Edition: | 1st ed. 2015. |
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| Online Access: | https://doi.org/10.1007/978-3-319-22506-7 |
Table of Contents:
- Preface
- Part I. Introduction to Measure and Integration.-1. Measurable Functions
- 2. Measure on a σ-Algebra
- 3. Integral of Nonnegative Functions
- 4. Integral of Real-Valued Functions
- 5. Banach Spaces Lp
- 6. Convergence of Functions
- 7. Decomposition of Measures
- 8. Extension of Measures
- 9. Product Measures
- Part II
- 10. Remarks on Integrals
- 11. Borel Measure
- 12. Representation Theorems
- 13. Invariant Measures
- References
- Index.