A first look at rigorous probability theory
by Rosenthal, Jeffrey S., (Jeffrey Seth)
"This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results."--Jacket.
Read More ↓Title Statements
- Full title :A first look at rigorous probability theory / Jeffrey S. Rosenthal.
Summary
"This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results."--Jacket.
Read More ↓Edition Statements
- Publication Date:©2006.
- Edition:2nd ed
Publication Statements
- Publisher(s):World Scientific
- Place of Publication:Singapore
- Language:eng
- Publication Date:©2006.
The Physical Object
- Description:1 online resource
Edition Identifiers
- ISBN:9789812772534, 9812772537
- oclc:on1020610856
- LC Classification:QA273
- Dewey Decimal:519.2
Table of Contents
Intro; Contents; Preface to the First Edition; Preface to the Second Edition; 1 The need for measure theory; 1.1 Various kinds of random variables; 1.2 The uniform distribution and non-measurable sets; 1.3 Exercises; 1.4 Section summary; 2 Probability triples; 2.1 Basic definition; 2.2 Constructing probability triples; 2.3 The Extension Theorem; 2.4 Constructing the Uniform[0 1] distribution; 2.5 Extensions of the Extension Theorem; 2.6 Coin tossing and other measures; 2.7 Exercises; 2.8 Section summary; 3 Further probabilistic foundations; 3.1 Random variables; 3.2 Independence.
3.3 Continuity of probabilities3.4 Limit events; 3.5 Tail fields; 3.6 Exercises; 3.7 Section summary; 4 Expected values; 4.1 Simple random variables; 4.2 General non-negative random variables; 4.3 Arbitrary random variables; 4.4 The integration connection; 4.5 Exercises; 4.6 Section summary; 5 Inequalities and convergence; 5.1 Various inequalities; 5.2 Convergence of random variables; 5.3 Laws of large numbers; 5.4 Eliminating the moment conditions; 5.5 Exercises; 5.6 Section summary; 6 Distributions of random variables; 6.1 Change of variable theorem; 6.2 Examples of distributions.
6.3 Exercises6.4 Sec…
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