Committee login






Small thumbnail

Secure Connected Objects

Small thumbnail

Banach, Fréchet, Hilbert and Neumann Spaces

Analysis for PDEs Set – Volume 1

Small thumbnail

Semi-Markov Migration Models for Credit Risk

Stochastic Models for Insurance Set – Volume 1

Small thumbnail

Human Exposure to Electromagnetic Fields

From Extremely Low Frequency (ELF) to Radio Frequency

Small thumbnail

Enterprise Interoperability


Small thumbnail

Data Treatment in Environmental Sciences

Multivaried Approach

Small thumbnail

From Pinch Methodology to Pinch-Exergy Integration of Flexible Systems

Thermodynamics – Energy, Environment, Economy Set

Small thumbnail

Exterior Algebras

Elementary Tribute to Grassmann's Ideas

Small thumbnail

Nonlinear Theory of Elastic Plates

Small thumbnail

Cognitive Approach to Natural Language Processing

Small thumbnail

Integral and Measure

From Rather Simple to Rather Complex

Vigirdas Mackevicius, Faculty of Mathematics of Vilnius University, Lithuania

ISBN: 9781848217690

Publication Date: August 2014   Hardback   300 pp.

130.00 USD

Add to cart


Ebook Ebook


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.


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.
18. Integral.
19. Product of Two Measure Spaces.

About the Authors

Vigirdas Mackevicius 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.


DownloadTable of Contents - PDF File - 35 Kb

Related Titles

0.02658 s.