Measure Theory: A First Course

ISBN-13: 9780123708991 / Angielski / Twarda / 2006 / 166 str.

Carlos S. Kubrusly

Opis

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.

• Designed with a minimum of prerequisites (intro analysis, and for Ch 5, linear algebra)
• Includes 140 classical measure-theory problems
• Carefully crafted to present essential elements of the theory in compact form

Recenzje

"As a book for a first course, the author has definitely come up with a well-balanced interesting text: not too threatening for beginners and interesting enough for someone with some knowledge of the subject." --Professor N. Levan, UCLA (USA)

Spis treści

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

O autorze

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.