Measures and probabilities

✍ Scribed by Michel Simonnet

• Publisher: Springer
• Year: 1996
• Tongue: English
• Leaves: 527
• Series: Universitext
• Edition: Softcover reprint of the original 1st ed. 1996
• Category: Library

✦ Synopsis

This book is intended to be an introductory, yet sophisticated, treatment of measure theory. It should provide an in-depth reference for the practicing mathematician. It is hoped that advanced students as well as instructors will find it useful. The first part of the book should prove useful to both analysts and probabilists. One may treat the second and third parts as an introduction to the theory of probability, or use the fourth part as an introduction to analysis.
The treatment is for the most part self-contained. Other than familiarity with general topology, some functional analysis and a certain degree of mathematical sophistication, little is required for profitable reading of this text. At the end of each chapter, exercises are provided which are designed to present some additional material and examples

✦ Table of Contents

Content: 1. Riesz Spaces --
2. Measures on Semirings --
3. Integrable and Measurable Functions --
4. Lebesgue Measure on R --
5. L[superscript p] Spaces --
6. Integrable Functions for Measures on Semirings --
7. Radon Measures --
8. Regularity --
9. Induced Measures and Product Measures --
10. Radon-Nikodym Derivatives --
11. Images of Measures --
12. Change of Variables --
13. Stieltjes Integral --
14. The Fourier Transform in R[superscript k] --
15. The Strong Law of Large Numbers --
16. The Central Limit Theorem --
17. Order Statistics --
18. Conditional Probability --
19. [mu]-Adequate Family of Measures --
20. Radon Measures Defined by Densities --
21. Images of Radon Measures and Product Measures --
22. Operations on Regular Measures --
23. Haar Measures --
24. Convolution of Measures.