Book:Marshall E. Munroe/Introduction to Measure and Integration
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Marshall E. Munroe: Introduction to Measure and Integration
Published $\text {1953}$
Subject Matter
Contents
- Chapter I. Point Set Theory
- 1. Sets and functions
- 2. Algebra of sets
- 3. Cardinal numbers
- 4. Metric spaces
- 5. Limits and continuity
- 6. Function spaces
- 7. Linear spaces
- 8. Additive classes and Borel sets
- 9. Category
- Chapter II. Measure — General Theory
- 10. Additive set functions
- 11. Outer measures
- 12. Regular outer measures
- 13. Metric outer measures
- Chapter III. Measure — Specific Examples
- 14. Lebesgue-Stieltjes measures
- *15. Probability
- *16. Hausdorff measures
- *17. Haar measure
- 18. Non-measurable sets
- Chapter IV. Measurable Functions
- 19. Definitions and basic properties
- 20. Operations on measurable functions
- 21. Approximation theorems
- *22. Stochastic variables
- Chapter V. Integration
- 23. The integral of a simple function
- 24. Integrable functions
- 25. Elementary properties of the integral
- 26. Additivity of the integral
- 27. Absolute continuity
- 28. Fubini's theorem
- *29. Expectation of a stochastic variable
- Chapter VI. Convergence Theorems
- 30. Uniform and almost everywhere convergence
- 31. Convergence in measure
- 32. Mean convergence
- 33. The Hölder and Minkowski inequalities
- 34. The $L_p$ spaces
- *35. Linear functionals on Banach spaces
- *36. Orthogonal expansions in Hilbert space
- *37. The mean ergodic theorem
- Chapter VII. Differentiation
- 38. Summary of the problem
- 39. Vitali coverings
- 40. Differentiation of additive set functions
- 41. The Lebesgue decomposition
- *42. Metric density and approximate continuity
- *43. Differentiation with respect to nets
- Bibliography
- Index of Postulates
- Index of Symbols
- Index