Measure and Integral

The Lebesgue integral is an essential tool in the fields of analysis and stochastics and for this reason, in many areas where mathematics is applied. This textbook is a concise, lecture-tested introduction to measure and integration theory. It addresses the important topics of this theory and presen...

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Main Authors: Brokate, Martin. (Author, http://id.loc.gov/vocabulary/relators/aut), Kersting, Götz. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
Edition:1st ed. 2015.
Series:Compact Textbooks in Mathematics,
Subjects:
Online Access:https://doi.org/10.1007/978-3-319-15365-0
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245 1 0 |a Measure and Integral  |h [electronic resource] /  |c by Martin Brokate, Götz Kersting. 
250 |a 1st ed. 2015. 
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300 |a VII, 172 p. 24 illus.  |b online resource. 
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505 0 |a Preface -- 1 Introduction -- 2 Measurability -- 3 Measures -- 4 The Integral of Nonnegative Functions -- 5 Integrable Functions -- 6 Convergence -- 7 Uniqueness and Regularity of Measures -- 8 Multiple Integrals and Product Measures -- 9 Absolute Continuity -- 10 The Transformation Formula of Jacobi -- 11 Construction of Measures -- 12 Hilbert Spaces -- 13 Banach Spaces -- Literature. 
520 |a The Lebesgue integral is an essential tool in the fields of analysis and stochastics and for this reason, in many areas where mathematics is applied. This textbook is a concise, lecture-tested introduction to measure and integration theory. It addresses the important topics of this theory and presents additional results which establish connections to other areas of mathematics. The arrangement of the material should allow the adoption of this textbook in differently composed Bachelor programmes. 
650 0 |a Measure theory. 
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