Measures and Probabilities

By: C.-M. Marle (Foreword by), Michel Simonnet

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Paperback | 1 July 1996

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528 Pages

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Integration theory holds a prime position, whether in pure mathematics or in various fields of applied mathematics. It plays a central role in analysis; it is the basis of probability theory and provides an indispensable tool in mathe matical physics, in particular in quantum mechanics and statistical mechanics. Therefore, many textbooks devoted to integration theory are already avail able. The present book by Michel Simonnet differs from the previous texts in many respects, and, for that reason, it is to be particularly recommended. When dealing with integration theory, some authors choose, as a starting point, the notion of a measure on a family of subsets of a set; this approach is especially well suited to applications in probability theory. Other authors prefer to start with the notion of Radon measure (a continuous linear func tional on the space of continuous functions with compact support on a locally compact space) because it plays an important role in analysis and prepares for the study of distribution theory. Starting off with the notion of Daniell measure, Mr. Simonnet provides a unified treatment of these two approaches.

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Non-Fiction Mathematics Algebra Probability & Statistics Calculus & Mathematical Analysis Topology Analytic Topology Mathematical Foundation Set Theory

Foreword
Preface
Riesz Spaces	p. 3
Measures on Semirings	p. 26
Integrable and Measurable Functions	p. 40
Lebesgue Measure on R	p. 86
L[superscript p] Spaces	p. 93
Integrable Functions for Measures on Semirings	p. 121
Radon Measures	p. 133
Regularity	p. 166
Induced Measures and Product Measures	p. 175
Radon-Nikodym Derivatives	p. 193
Images of Measures	p. 224
Change of Variables	p. 242
Stieltjes Integral	p. 265
The Fourier Transform in R[superscript k]	p. 286
The Strong Law of Large Numbers	p. 311
The Central Limit Theorem	p. 326
Order Statistics	p. 344
Conditional Probability	p. 352
[mu]-Adequate Family of Measures	p. 379
Radon Measures Defined by Densities	p. 397
Images of Radon Measures and Product Measures	p. 408
Operations on Regular Measures	p. 416
Haar Measures	p. 425
Convolution of Measures	p. 465
Index	p. 499
Symbol Index	p. 505
Table of Contents provided by Blackwell. All Rights Reserved.

Measures and Probabilities

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Paperback

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