Analysis and probability
Probability theory is a rapidly expanding field and is used in many areas of science and technology. Beginning from a basis of abstract analysis, this mathematics book develops the knowledge needed for advanced students to develop a complex understanding of probability. The first part of the book sy...
| Autor principal: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; Boston :
Elsevier
2013
London : 2013. |
| Edición: | 1st ed |
| Colección: | Elsevier insights.
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009628580606719 |
Tabla de Contenidos:
- Analysis and Probability; Analysis and Probability; Copyright; Contents; Preface; PART ONE: ANALYSIS; Elements of Set Theory; 1 Sets and Operations on Sets; 2 Functions and Cartesian Products; 3 Equivalent Relations and Partial Orderings; References; Topological Preliminaries; 4 Construction of Some Topological Spaces; 5 General Properties of Topological Spaces; 6 Metric Spaces; Measure Spaces; 7 Measurable Spaces; 8 Measurable Functions; 9 Definitions and Properties of the Measure; 10 Extending Certain Measures; The Integral; 11 Definitions and Properties of the Integral
- 12 Radon-Nikodým Theorem and the Lebesgue Decomposition13 The Spaces Lp; 14 Convergence for Sequences of Measurable Functions; Measures on Product σ-Algebras; 15 The Product of a Finite Number of Measures; 16 The Product of Infinitely Many Measures; PART TWO: PROBABILITY; Elementary Notions in Probability Theory; 17 Events and Random Variables; 18 Conditioning and Independence; Distribution Functions and Characteristic Functions; 19 Distribution Functions; 20 Characteristic Functions; Reference; Probabilities on Metric Spaces; 21 Probabilities in a Metric Space
- 22 Topology in the Space of ProbabilitiesCentral Limit Problem; 23 Infinitely Divisible Distribution/Characteristic Functions; 24 Convergence to an Infinitely Divisible Distribution/Characteristic Function; Reference; Sums of Independent Random Variables; 25 Weak Laws of Large Numbers; 26 Series of Independent Random Variables; 27 Strong Laws of Large Numbers; 28 Laws of the Iterated Logarithm; Conditioning; 29 Conditional Expectations, Conditional Probabilities and Conditional Independence; 30 Stopping Times and Semimartingales; Ergodicity, Mixing, and Stationarity; 31 Ergodicity and Mixing
- 32 Stationary SequencesList of Symbols
