A modern theory of integration robert bartle [pdf]
Modern Theory of Integration by Robert G. Bartle
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About this book :-
Modern Theory of Integration written by
Robert G. Bartle
It is hardly possible to overemphaize the importance of the theory of integration to mathemtical analysis, inded it is one of the twin pillars on which analysis is built. Granting that it is suprising that new devlopments continue to arise in this theory, which was originated by the great Newton and Leibuiz over three centruies ago, made rigorous by Riemann in the middle of the nineteenth century and extended by Lebesgue at the begining of the twentieth century.
(Robert G. Bartle)
Book Detail :-
Title: Modern Theory of Integration
Edition:
Author(s): Robert G. Bartle
Publisher: American Mathematical Society
Series: Graduate Studies in Mathematics
Year: 2001
Pages: 457
Type: PDF
Language: English
ISBN: 0821808451,9780821808450
Country: US
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About Author :-
Author Robert Gardner Bartle (1927–2003) was an American mathematician. He was specializing in real analysis. He is known for writing the popular textbooks The Elements of Real Analysis (1964), The Elements of Integration (1966), and Introduction to Real Analysis (2011) published by John Wiley & Sons.
Bartle was born in Kansas City, Missouri, and was the son of Glenn G. Bartle and Wanda M. Bartle. He was married to Doris Sponenberg Bartle (born 1927) from 1952 to 1982 and they had two sons, James A. Bartle (born 1955) and John R. Bartle (born 1958). He was on the faculty of the Department of Mathematics at the University of Illinois from 1955 to 1990.
Bartle was Executive Editor of Mathematical Reviews from 1976 to 1978 and from 1986 to 1990. From 1990 to 1999 he taught at Eastern Michigan University. In 1997, he earned a writing award from the Mathematical Association of America for his paper "Return to the Riemann Integral".[1]
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Book Contents :-
Modern Theory of Integration written by
Robert G. Bartle
cover the following topics.
1. Gauges and Integrals
2. Some Examples
3. Basic properties of the Integral
4. The Fundamental Theorems of Calculus
5. The Sakes Henstock lemma
6. Measurable functions
7. Absolute integrability
8. Covergence theorems
9. Integrability and mean covergence
10. Measure, mearurability and multipliers
11. Modes of convergence
12. Applications to calculus
13. Substituion theorems
14. Absolute continuity
16. Infinite Intervals
18. Measurable sets
19. Measurable funcitons
20. Sequences of functions
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