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An introduction to measure-theoretic probability /
"In this introductory chapter, the concepts of a field and of a [sigma]-field are introduced, they are illustrated bymeans of examples, and some relevant basic results are derived. Also, the concept of a monotone class is defined and its relationship to certain fields and [sigma]-fields is inve...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; New York :
Academic Press, an imprint of Elsevier,
2014.
|
| Edición: | Second edition. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | SCIDIR_ocn876589188 | ||
| 003 | OCoLC | ||
| 005 | 20231120111549.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 140414s2014 ne ob 001 0 eng d | ||
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| 016 | 7 | |a 016709723 |2 Uk | |
| 019 | |a 1105183531 |a 1105567426 | ||
| 020 | |a 9780128002902 |q (electronic bk.) | ||
| 020 | |a 0128002905 |q (electronic bk.) | ||
| 020 | |z 9780128000427 | ||
| 035 | |a (OCoLC)876589188 |z (OCoLC)1105183531 |z (OCoLC)1105567426 | ||
| 050 | 4 | |a QA273 |b .R864 2014eb | |
| 082 | 0 | 4 | |a 519.2 |2 23 |
| 100 | 1 | |a Roussas, George G., |e author. | |
| 245 | 1 | 3 | |a An introduction to measure-theoretic probability / |c by George G. Roussas. |
| 250 | |a Second edition. | ||
| 264 | 1 | |a Amsterdam ; |a New York : |b Academic Press, an imprint of Elsevier, |c 2014. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 520 | |a "In this introductory chapter, the concepts of a field and of a [sigma]-field are introduced, they are illustrated bymeans of examples, and some relevant basic results are derived. Also, the concept of a monotone class is defined and its relationship to certain fields and [sigma]-fields is investigated. Given a collection of measurable spaces, their product space is defined, and some basic properties are established. The concept of a measurable mapping is introduced, and its relation to certain [sigma]-fields is studied. Finally, it is shown that any random variable is the pointwise limit of a sequence of simple random variables"-- |c Provided by publisher | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Certain classes of sets, measurability, and pointwise approximation -- Definition and construction of a measure and its basic properties -- Some modes of convergence of sequences of random variables and their relationships -- The integral of a random variable and its basic properties -- Standard convergence theorems, the Fubini theorem -- Standard moment and probability inequalities, convergence in the rth mean and its implications -- The Hahn-Jordan decomposition theorem, the Lebesgue decomposition theorem, and the Radon-Nikodym theorem -- Distribution functions and their basic properties, Helly-Bray type results -- Conditional expectation and conditional probability, and related properties and results -- Independence -- Topics from the theory of characteristic functions -- The central limit problem: the centered case -- The central limit problem: the noncentered case -- Topics from sequences of independent random variables -- Topics from Ergodic theory -- Two cases of statistical inference: estimation of a real-valued parameter, nonparametric estimation of a probability density function -- Appendixes: A. Brief review of chapters 1-16 -- B. Brief review of Riemann-Stieltjes integral -- C. Notation and abbreviations. | |
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Measure theory. | |
| 650 | 6 | |a Probabilit�es. |0 (CaQQLa)201-0011592 | |
| 650 | 6 | |a Th�eorie de la mesure. |0 (CaQQLa)201-0005696 | |
| 650 | 7 | |a probability. |2 aat |0 (CStmoGRI)aat300055653 | |
| 650 | 7 | |a Measure theory |2 fast |0 (OCoLC)fst01013175 | |
| 650 | 7 | |a Probabilities |2 fast |0 (OCoLC)fst01077737 | |
| 776 | 0 | 8 | |i Print version: |a Roussas, George G. |t Introduction to measure-theoretic probability. |b Second edition |z 9780128000427 |w (DLC) 2014007243 |w (OCoLC)868642456 |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780128000427 |z Texto completo |