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Field name	Details
Dewey Class	519.2
Title	Measure, Integral and Probability ([EBook] /) / by Marek Capiński, Peter Ekkehard Kopp.
Author	Capiński, Marek
Added Personal Name	Kopp, Peter Ekkehard author.
Other name(s)	SpringerLink (Online service)
Edition statement	Second Edition.
Publication	London : : Springer London, , 2004.
Physical Details	XV, 311 p. 3 illus. : online resource.
Series	Springer undergraduate mathematics series 1615-2085
ISBN	9781447106456
Summary Note	Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: · a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales · key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.:
Contents note	Content -- 1. Motivation and preliminaries -- 1.1 Notation and basic set theory -- 1.2 The Riemann integral: scope and limitations -- 1.3 Choosing numbers at random -- 2. Measure -- 2.1 Null sets -- 2.2 Outer measure -- 2.3 Lebesgue-measurable sets and Lebesgue measure -- 2.4 Basic properties of Lebesgue measure -- 2.5 Borel sets -- 2.6 Probability -- 2.7 Proofs of propositions -- 3. Measurable functions -- 3.1 The extended real line -- 3.2 Lebesgue-measurable functions -- 3.3 Examples -- 3.4 Properties -- 3.5 Probability -- 3.6 Proofs of propositions -- 4. Integral -- 4.1 Definition of the integral -- 4.2 Monotone convergence theorems -- 4.3 Integrable functions -- 4.4 The dominated convergence theorem -- 4.5 Relation to the Riemann integral -- 4.6 Approximation of measurable functions -- 4.7 Probability -- 4.8 Proofs of propositions -- 5. Spaces of integrable functions -- 5.1 The space L1 -- 5.2 The Hilbert space L2 -- 5.3 The LP spaces: completeness -- 5.4 Probability -- 5.5 Proofs of propositions -- 6. Product measures -- 6.1 Multi-dimensional Lebesgue measure -- 6.2 Product ?-fields -- 6.3 Construction of the product measure -- 6.4 Fubini’s theorem -- 6.5 Probability -- 6.6 Proofs of propositions -- 7. The Radon—Nikodym theorem -- 7.1 Densities and conditioning -- 7.2 The Radon—Nikodym theorem -- 7.3 Lebesgue—Stieltjes measures -- 7.4 Probability -- 7.5 Proofs of propositions -- 8. LimitL theorems -- 8.1 Modes of convergence -- 8.2 Probability -- 8.3 Proofs of propositions -- Solutions -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4471-0645-6
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Economics, Mathematical . Mathematical analysis . Mathematics . Measure and Integration . Measure theory . Probabilities . Probability theory and stochastic processes . Quantitative Finance . Authors: Capiński, Marek . Kopp, Peter Ekkehard . Corporate Authors: SpringerLink (Online service) . Series: Springer undergraduate mathematics series . Classification: 519.2 .

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Measure, Integral and Probability

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