Measure and Integral electronic resource by Martin Brokate, Götz Kersting.
Material type: TextSeries: Compact Textbooks in MathematicsPublication details: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015Description: VII, 172 p. 24 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319153650Subject(s): mathematics | Measure theory | Mathematics | Measure and IntegrationDDC classification: 515.42 LOC classification: QA312-312.5Online resources: Click here to access onlinePreface -- 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.
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.
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