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Probability measures on metric spaces

Author: K R Parthasarathy
Publisher: New York : Academic Press, ©1967.
Series: Probability and mathematical statistics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Probability Measures on Metric Spaces.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Parthasarathy, K.R.
Probability Measures on Metric Spaces.
New York : Academic Press, 1967
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: K R Parthasarathy
ISBN: 9781483225258 1483225259
OCLC Number: 898772095
Description: 1 online resource (289 pages).
Contents: Fron Cover; Probability Measures on Metric Spaces; Copyright Page; Preface; Table of Contents; ChapterI. The Borel Subsets of a Metric Space; 1. General Properties of Borel Sets; 2. The Isomorphism Theorem; 3. The Kuratowski Theorem; 4. Borel Cross Sections in Compact Metric Spaces; 5. Borel Cross Sections in Locally Compact Groups; ChapterII. Probability Measures in a Metric Space; 1. Regular Measures; 2. Spectrum of a Measure; 3. Tight Measures; 4. Perfect Measures; 5. Linear Functionals and Measures; 6. The Weak Topology in the Space of Measures; 7. Convergence of Sample Distributions. 8. Existence of Nonatomic Measures in Metric SpacesChapterIII. Probability Measures in a Metric Group; 1. The Convolution Operation; 2. Shift Compactness in M(X); 3. Idempotent Measures; 4. Indecomposable Measures; 5. The Case When X Is Abelian; Chapter VI. Probability Measures in Locally Compact Abelian Groups; 1. Introduction; 2. Preliminary Facts about a Group and Its Character Group ; 3. Measures and Their Fourier Transforms; 4. Infinitely Divisible Distributions; 5. General Limit Theorems for Sums of Infinitesimal Summands ; 6. Gaussian Distributions. 7. Representation of Infinitely Divisible Distributions8. Uniqueness of the Representation; 9. Compactness Criteria; 10. Representation of Convolution Semigroups; 11. A Decomposition Theorem; 12. Absolutely Continuous Indecomposable Distributions in X ; ChapterV. The Kolmogorov Consistency Theorem and Conditional Probability; 1. Statement of the First Problem; 2. Standard Borel Spaces; 3. The Consistency Theorem in the Case of Inverse Limits of Borel Spaces; 4. The Extension Theorem; 5. The Kolmogorov Consistency Theorem; 6. Statement of the Second Problem. 7. Existence of Conditional Probability8. Regular Conditional Probability; ChapterVI. Probability Measures in a Hilbert Space; 1. Introduction; 2. Characteristic Functions and Compactness Criteria; 3. An Estimate of the Variance; 4. Infinitely Divisible Distributions; 5. Compactness Criteria; 6. Accompanying Laws; 7. Representation of Convolution Semigroups; 8. Decomposition Theorem; 9. Ergodic Theorems; ChapterVII. Probability Measures on C[0, 1] and D[0, 1]; 1. Introduction; 2. Probability Measures on C[0, 1]; 3. A Condition for the Realization of a Stochastic Process inC. 4. Convergence to Brownian Motion5. Distributions of Certain Random Variables Associated with the Brownian Motion; 7. Probability Measures inD; 8. Ergodic Theorems for D-Valued Random Variables; 9. Applications to Statistical Tests of Hypothesis; Bibliographical Notes; Bibliography; List of Symbols; Author Index; Subject Index.
Series Title: Probability and mathematical statistics.
Responsibility: K.R. Parthasarathy.

Abstract:

Probability Measures on Metric Spaces.

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