Real analysis and probability / R.M. Dudley.
Dudley, R. M. (Richard M.)| Call Number | 515 |
| Author | Dudley, R. M. author. |
| Title | Real analysis and probability / R.M. Dudley. Real Analysis & Probability |
| Edition | Second edition. |
| Physical Description | 1 online resource (x, 555 pages) : digital, PDF file(s). |
| Series | Cambridge studies in advanced mathematics ; 74 |
| Notes | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| Summary | This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution. |
| Subject | MATHEMATICAL ANALYSIS. FUNCTIONS OF REAL VARIABLES. PROBABILITIES. |
| Multimedia |
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| Summary | This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution. |
| Notes | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| Subject | MATHEMATICAL ANALYSIS. FUNCTIONS OF REAL VARIABLES. PROBABILITIES. |
| Multimedia |