• Integral And Measure. From Rather Simple To Rather Complex

Integral And Measure. From Rather Simple To Rather Complex

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Описание

This book is devoted to integration, one of the two main operations in calculus

Based on the latter, in Part 2, the author develops a theory of integration for functions of several variables

However, Part 1 can be successfully used by any student as a simple introduction to integration 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

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

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

The book is mainly devoted to students of mathematics and related specialities

The majority of chapters are complemented with problems, mostly of the theoretical type

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