Integral And Measure: From Rather Simple To Rather Complex Hardcover

Vigirdas Mackevicius

This book is devoted to integration, one of the two main operations in calculus. In Part 1, the definition of the integral of a one-variable function is different (not essentially, but rather methodically) from traditional definitions of Riemann or Lebesgue integrals. Such an approach allows us, on the one hand, to quickly develop the practical skills of integration as well as, on the other hand, in Part 2, to pass naturally to the more general Lebesgue integral. Based on the latter, in Part 2, the author develops a theory of integration for functions of several variables. In Part 3, within the same methodological scheme, the author presents the elements of theory of integration in an abstract space equipped with a measure; we cannot do without this in functional analysis, probability theory, etc. The majority of chapters are complemented with problems, mostly of the theoretical type. The book is mainly devoted to students of mathematics and related specialities. However, Part 1 can be successfully used by any student as a simple introduction to integration calculus.

1848217692

9781848217690

English

ISTE Ltd and John Wiley & Sons Inc

6 October 2014

300

Vigirdas MACKEVI IUS is Professor of the Department of Mathematical Analysis in the Faculty of Mathematics of Vilnius University in Lithuania. His research interests include stochastic analysis, limit theorems for stochastic processes, and stochastic numerics.

We have to mention here that since some of the problems are of a theoretical nature, while others are direct computations or applications of the theory, the book addresses both students who want a quick introduction to integrals and their use in real analysis and students who want to understand the mechanism behind an integration theory built on some measure space. (Mathematical Reviews, 1 October 2015)