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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Sp�ataru, Aurel (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam : Elsevier, 2013.
Edición:First edition.
Colección:Elsevier insights.
Temas:
Acceso en línea:Texto completo

MARC

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100 1 |a Sp�ataru, Aurel,  |e author. 
245 1 0 |a Analysis and probability /  |c Aurel Sp�ataru, Romanian Academy, Bucharest, Romania. 
250 |a First edition. 
264 1 |a Amsterdam :  |b Elsevier,  |c 2013. 
300 |a 1 online resource (x, 448 pages) 
336 |a text  |b txt  |2 rdacontent 
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505 0 |6 880-01  |a pt. 1. Analysis -- 1. Elements of Set Theory -- 2. Topological Preliminaries -- 3. Measure Spaces -- 4. The Integral -- 5. Measures on Product v-Algebras -- pt. 2. Probability -- 6. Elementary Notions in Probability Theory -- 7. Distribution Functions and Characteristic Functions -- 8. Probabilities on Metric Spaces -- 9. Central Limit Problem -- 10. Sums of Independent Random Variables -- 11. Conditioning -- 12. Ergodicity, Mixing, and Stationarity. 
520 |a 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 systematically presents concepts and results from analysis before embarking on the study of probability theory. The initial section will also be useful for those interested in topology, measure theory, real analysis and functional analysis. The second part of the book presents the concepts, methodology. 
588 0 |a Print version record. 
650 0 |a Stochastic analysis. 
650 0 |a Probabilities. 
650 4 |a Stochastic analysis. 
650 6 |a Analyse stochastique.  |0 (CaQQLa)201-0002662 
650 6 |a Probabilit�es.  |0 (CaQQLa)201-0011592 
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650 7 |a Probabilities.  |2 fast  |0 (OCoLC)fst01077737 
650 7 |a Stochastic analysis.  |2 fast  |0 (OCoLC)fst01133499 
776 0 8 |i Print version:  |a Sp�ataru, Aurel.  |t Analysis and probability.  |b 1st ed.  |d Amsterdam ; Boston : Elsevier Science, 2013  |z 9780124016651  |w (OCoLC)838047736 
830 0 |a Elsevier insights. 
856 4 0 |u https://sciencedirect.uam.elogim.com/science/book/9780124016651  |z Texto completo 
880 0 0 |6 505-01/(S  |g Machine generated contents note:  |g pt. One  |t Analysis --  |g 1.  |t Elements of Set Theory --  |g Section 1  |t Sets and Operations on Sets --  |g Section 2  |t Functions and Cartesian Products --  |g Section 3  |t Equivalent Relations and Partial Orderings --  |t References --  |g 2.  |t Topological Preliminaries --  |g Section 4  |t Construction of Some Topological Spaces --  |g Section 5  |t General Properties of Topological Spaces --  |g Section 6  |t Metric Spaces --  |g 3.  |t Measure Spaces --  |g Section 7  |t Measurable Spaces --  |g Section 8  |t Measurable Functions --  |g Section 9  |t Definitions and Properties of the Measure --  |g Section 10  |t Extending Certain Measures --  |g 4.  |t Integral --  |g Section 11  |t Definitions and Properties of the Integral --  |g Section 12  |t Radon-Nikodym Theorem and the Lebesgue Decomposition --  |g Section 13  |t Spaces --  |g Section 14  |t Convergence for Sequences of Measurable Functions --  |g 5.  |t Measures on Product σ-Algebras --  |g Section 15  |t Product of a Finite Number of Measures --  |g Section 16  |t Product of Infinitely Many Measures --  |g pt. Two  |t Probability --  |g 6.  |t Elementary Notions in Probability Theory --  |g Section 17  |t Events and Random Variables --  |g Section 18  |t Conditioning and Independence --  |g 7.  |t Distribution Functions and Characteristic Functions --  |g Section 19  |t Distribution Functions --  |g Section 20  |t Characteristic Functions --  |t References --  |g 8.  |t Probabilities on Metric Spaces --  |g Section 21  |t Probabilities in a Metric Space --  |g Section 22  |t Topology in the Space of Probabilities --  |g 9.  |t Central Limit Problem --  |g Section 23  |t Infinitely Divisible Distribution/Characteristic Functions --  |g Section 24  |t Convergence to an Infinitely Divisible Distribution/Characteristic Function --  |t References --  |g 10.  |t Sums of Independent Random Variables --  |g Section 25  |t Weak Laws of Large Numbers --  |g Section 26  |t Series of Independent Random Variables --  |g Section 27  |t Strong Laws of Large Numbers --  |g Section 28  |t Laws of the Iterated Logarithm --  |g 11.  |t Conditioning --  |g Section 29  |t Conditional Expectations, Conditional Probabilities, and Conditional Independence --  |g Section 30  |t Stopping Times and Semimartingales --  |g 12.  |t Ergodicity, Mixing, and Stationarity --  |g Section 31  |t Ergodicity and Mixing --  |g Section 32  |t Stationary Sequences.