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Measure and Integral
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Artikel-Nr:
9783319153650
Veröffentl:
2015
Einband:
eBook
Seiten:
172
Autor:
Martin Brokate
eBook Typ:
PDF
eBook Format:
eBook
Kopierschutz:
Digital Watermark [Social-DRM]
Sprache:
Englisch
Beschreibung:
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.
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.
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.