Measure and Integral [Paperback]

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.Martin Brokate is Professor for Mathematical Modelling at TU Munich, Germany. G?tz Kersting is Professor for Stochastics at the Goethe University in Frankfurt / Main, Germany.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.

New?arrangement of the subject matter with hands-on examples

Concise presentation of the material

Provides?guidance and material for different variants of?2-hour?courses

Focuses on the essentials of measure and integration theory

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