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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...
| Cote: | Libro Electrónico |
|---|---|
| Auteur principal: | |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
Amsterdam ; New York :
Academic Press, an imprint of Elsevier,
2014.
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| Édition: | Second edition. |
| Sujets: | |
| Accès en ligne: | Texto completo |
Table des matières:
- 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.