The generalized Riemann integral

by McLeod, Robert M.

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Title Statements

Full title :The generalized Riemann integral / by Robert M. McLeod.

Edition Statements

Publication Date:©1980.

Publication Statements

Publisher(s):Mathematical Association of America
Place of Publication:Washington, D.C
Language:eng
Publication Date:©1980.

The Physical Object

Description:1 online resource (xiii, 275 pages) : : illustrations

Edition Identifiers

ISBN:9781614440208, 1614440204
oclc:ocn610409753
LC Classification:QA311
Dewey Decimal:515.43

Front Cover -- The Generalized Riemann Integral -- Copyright Page -- Contents -- Preface -- List of Symbols -- Introduction -- Chapter 1â€?Definition of the Generalized Riemann Integral -- 1.1 Selecting Riemann sums -- 1.2 Definition of the generalized Riemann integral -- 1.3 Integration over unbounded intervals -- 1.4 The fundamental theorem of calculus -- 1.5 The status of improper integrals -- 1.6 Multiple integrals -- 1.7 Sum of a series viewed as an integral -- S1.8 The limit based on gauges -- S1.9 Proof of the fundamental theorem -- 1.10 Exercises

Chapter 2â€?Basic Properties of the Integral2.1 The integral as a function of the integrand -- 2.2 The Cauchy criterion -- 2.3 Integrability on subintervals -- 2.4 The additivity of integrals -- 2.5 Finite additivity of functions of intervals -- 2.6 Continuity of integrals. Existence of primitives -- 2.7 Change of variables in integrals on intervals in R -- S2.8 Limits of integrals over expanding intervals -- 2.9 Exercises -- Chapter 3â€?Absolute Integrability and Convergence Theorems -- 3.1 Henstock's lemma

3.2 Integrability of the absolute value of an integrable function3.3 Lattice operations on integrable functions -- 3.4 Uni…