Introduction to gauge integrals / Charles Swartz.

Format:

Book

Author/Creator:

Swartz, Charles, 1938-

Language:

English

Subjects (All):

Henstock-Kurzweil integral.

Calculus.

Physical Description:

1 online resource (150p.)

Edition:

1st ed.

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, c2001.

Language Note:

English

Summary:

A presentation of the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. A basic knowledge of introductory real analysis is required of the reader. This book presents the Henstock-Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock-Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces.;A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc.

Contents:

Introduction to the gauge or Henstock-Kurzweil integral; basic properties of the gauge integral; Henstock's Lemma and improper integrals; the gauge integral over unbounded intervals; convergence theorems; integration over more general sets -Lebesgue measure; the space of gauge integrable functions; multiple integrals and Fubini's theorem; the McShane integral; McShane integrability is equivalent to absolute Henstock-Kurzweil integrability.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 149-153) and index.

ISBN:

9786611956318

9781281956316

1281956317

9789812810656

981281065X

OCLC:

815755944