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Integral and measure : from rather simple to rather complex / Vigirdas Mackevicius.

By: Material type: TextTextSeries: Mathematics and statistics seriesPublication details: Hoboken, NJ : John Wiley, 2014.Description: xiv, 281 p. : illustrations ; 24 cmISBN:
  • 9781848217690
Subject(s): DDC classification:
  • 515.42 23 M157
Contents:
Part 1: Integration of one-variable functions -- 1. Functions without second-kind discontinuities -- 2. Indefinite integral -- 3. Definite integral -- 4. Applications of the integral -- 5. Other definitions: Riemann and Stieltjes integrals -- 6. Improper integrals -- Part 2: Integration of several-variable functions -- 7. Additional properties of step functions -- 8. Lebesgue integral -- 9. Fubini and change-of-variables theorems -- 10. Applications of multiple integrals -- 11. Parameter-dependent integrals -- Part 3: Measure and integration in a measure space -- 12. Families of sets -- 13. Measure spaces -- 14. Extension of measure -- 15. Lebesgue-Stieltjes measures on the real line and distribution functions --- 16. Measurable mappings and real measurable functions -- 17. Convergence almost everywhere and convergence in measure -- 18. Integral -- 19. Product of two measure spaces -- Bibliography -- Index.
Summary: 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515.42 M157 (Browse shelf(Opens below)) Available 136641
Total holds: 0

Includes bibliographical references and index.

Part 1: Integration of one-variable functions --
1. Functions without second-kind discontinuities --
2. Indefinite integral --
3. Definite integral --
4. Applications of the integral --
5. Other definitions: Riemann and Stieltjes integrals --
6. Improper integrals --

Part 2: Integration of several-variable functions --
7. Additional properties of step functions --
8. Lebesgue integral --
9. Fubini and change-of-variables theorems --
10. Applications of multiple integrals --
11. Parameter-dependent integrals --

Part 3: Measure and integration in a measure space --
12. Families of sets --
13. Measure spaces --
14. Extension of measure --
15. Lebesgue-Stieltjes measures on the real line and distribution functions ---
16. Measurable mappings and real measurable functions --
17. Convergence almost everywhere and convergence in measure --
18. Integral --
19. Product of two measure spaces --
Bibliography --
Index.

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.

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