Measure Theory

Klappentext This contemporary first course focuses on concepts and ideas of Measure Theory! highlighting the theoretical side of the subject. Its primary intention is to introduce Measure Theory to a new generation of students! whether in mathematics or in one of the sciences! by offering them on the one hand a text with complete! rigorous and detailed proofs--sketchy proofs have been a perpetual complaint! as demonstrated in the many Amazon reader reviews critical of authors who omit 'trivial' steps and make not-so-obvious 'it is obvious' remarks. On the other hand! Kubrusly offers a unique collection of fully hinted problems. On the other hand! Kubrusly offers a unique collection of fully hinted problems. The author invites the readers to take an active part in the theory construction! thereby offering them a real chance to acquire a firmer grasp on the theory they helped to build. These problems! at the end of each chapter! comprise complements and extensions of the theory! further examples and counterexamples! or auxiliary results. They are an integral part of the main text! which sets them apart from the traditional classroom or homework exercises.JARGON BUSTER: measure theory Measure theory investigates the conditions under which integration can take place.It considers various ways in which the size of a set can be estimated.This topic is studied in pure mathematics programs but the theory is also foundational for students of statistics and probability! engineering! and financial engineering. Zusammenfassung Measure theory investigates the conditions under which integration can take place. It considers various ways in which the 'size' of a set can be estimated. This title focuses on concepts and ideas of Measure Theory! highlighting the theoretical side of the subject. It invites the readers to take an active part in the theory construction. Inhaltsverzeichnis Measurability; Measure; Integral; Integrability; Spaces L^p; Convergence; Decomposition; Extension; Product ...

Autorentext
Carlos Kubrusly was born in Rio de Janeiro in November 1947. He received his Ph.D. from the University of Warwick in 1976, held postdoctoral visiting research positions at the Universities of Warwick and Bonn, and has been a faculty member of Catholic University of Rio de Janeiro since 1972, where he became a full professor in 1988. Professor Kubrusly has published over a hundred scientific articles in international journals and proceedings of international conferences. He has participated in about forty scientific conferences, all with paper presentation, including plenary sections at the Toulouse IFAC Symposium in 1982 and at the Newport Beach SOTA Conference in 1998, and has also been a member of program committees of several international conferences.

Zusammenfassung
Measure theory investigates the conditions under which integration can take place. It considers various ways in which the 'size' of a set can be estimated. This title focuses on concepts and ideas of Measure Theory, highlighting the theoretical side of the subject. It invites the readers to take an active part in the theory construction.

Inhalt
Measurability; Measure; Integral; Integrability; Spaces L^p; Convergence; Decomposition; Extension; Product