UID:
almafu_9960073769902883
Umfang:
1 online resource (x, 448 pages).
Ausgabe:
1st ed.
ISBN:
9781283970303
,
1283970309
,
9780124017276
,
0124017274
Serie:
Elsevier insights
Inhalt:
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, methodo
Anmerkung:
Description based upon print version of record
,
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
,
English
Weitere Ausg.:
ISBN 9780323282635
Weitere Ausg.:
ISBN 0323282636
Weitere Ausg.:
ISBN 9780124016651
Weitere Ausg.:
ISBN 0124016650
Sprache:
Englisch
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