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, District of Columbia
Language:eng
Publication Date:©1980

The Physical Object

Description:1 online resource (290 pages) : : illustrations, tables

Edition Identifiers

ISBN:9781614440208, 1614440204, 0883850451, 9780883850459, 0883850214, 9780883850213
oclc:on1097153278
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 Integral""""2.1 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 integrab…