Measures, integrals and martingales / René L. Schilling.

Call Number	515.42
Author	Schilling, René L., author.
Title	Measures, integrals and martingales / René L. Schilling. Measures, Integrals & Martingales
Physical Description	1 online resource (x, 381 pages) : digital, PDF file(s).
Notes	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Contents	Prologue -- The pleasures of counting -- [sigma]-algebras -- Measures -- Uniqueness of measures -- Existence of measures -- Measurable mappings -- Measurable functions -- Integration of positive functions -- Integrals of measurable functions and null sets -- Convergence theorems and their applications -- The function spaces [actual symbol not reproducible] -- Product measures and Fubini's theorem -- Integrals with respect to image measures -- Integrals of images and Jacobi's transformation rule -- Uniform integrability and Vitali's convergence theorem -- Martingales -- Martingale convergence theorems.
Summary	This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability theory. The basic theory - measures, integrals, convergence theorems, Lp-spaces and multiple integrals - is explored in the first part of the book. The second part then uses the notion of martingales to develop the theory further, covering topics such as Jacobi's generalized transformation Theorem, the Radon-Nikodym theorem, Hardy-Littlewood maximal functions or general Fourier series. Undergraduate calculus and an introductory course on rigorous analysis are the only essential prerequisites, making this text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included and these are not merely drill problems but are there to consolidate what has already been learnt and to discover variants, sideways and extensions to the main material. Hints and solutions can be found on the author's website, which can be reached from www.cambridge.org/9780521615259.
Subject	MEASURE THEORY. INTEGRALS. MARTINGALES (MATHEMATICS)
Multimedia	https://doi.org/10.1017/CBO9780511810886

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$a This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability theory. The basic theory - measures, integrals, convergence theorems, Lp-spaces and multiple integrals - is explored in the first part of the book. The second part then uses the notion of martingales to develop the theory further, covering topics such as Jacobi's generalized transformation Theorem, the Radon-Nikodym theorem, Hardy-Littlewood maximal functions or general Fourier series. Undergraduate calculus and an introductory course on rigorous analysis are the only essential prerequisites, making this text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included and these are not merely drill problems but are there to consolidate what has already been learnt and to discover variants, sideways and extensions to the main material. Hints and solutions can be found on the author's website, which can be reached from www.cambridge.org/9780521615259.

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Summary	This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability theory. The basic theory - measures, integrals, convergence theorems, Lp-spaces and multiple integrals - is explored in the first part of the book. The second part then uses the notion of martingales to develop the theory further, covering topics such as Jacobi's generalized transformation Theorem, the Radon-Nikodym theorem, Hardy-Littlewood maximal functions or general Fourier series. Undergraduate calculus and an introductory course on rigorous analysis are the only essential prerequisites, making this text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included and these are not merely drill problems but are there to consolidate what has already been learnt and to discover variants, sideways and extensions to the main material. Hints and solutions can be found on the author's website, which can be reached from www.cambridge.org/9780521615259.
Notes	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Contents	Prologue -- The pleasures of counting -- [sigma]-algebras -- Measures -- Uniqueness of measures -- Existence of measures -- Measurable mappings -- Measurable functions -- Integration of positive functions -- Integrals of measurable functions and null sets -- Convergence theorems and their applications -- The function spaces [actual symbol not reproducible] -- Product measures and Fubini's theorem -- Integrals with respect to image measures -- Integrals of images and Jacobi's transformation rule -- Uniform integrability and Vitali's convergence theorem -- Martingales -- Martingale convergence theorems.
Subject	MEASURE THEORY. INTEGRALS. MARTINGALES (MATHEMATICS)
Multimedia	https://doi.org/10.1017/CBO9780511810886