Introduction to gauge integrals

Charles S. Swartz

158 pages, parution le 06/12/2001

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Résumé

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

L'auteur - Charles S. Swartz

CHARLES S. SWARTZ oversees efforts at the Entertainment Technology Center at USC to further the entertainment industry through new technology. He draws from more than two decades of experience in feature film and television production, academic programming and strategic consulting to lead the center in identifying emerging entertainment technology issues and developing projects to study them. Swartz assumed his current position of Executive Director/CEO in 2OO2, where he has refocused and recharged the research center, l-le serves as SMPTE Governor representing the Hollywood Region. In 1996, the Los Angeles Business Journal named him one of 1OO technology leaders in Los Angeles.

Caractéristiques techniques

	PAPIER
Éditeur(s)	World Scientific
Auteur(s)	Charles S. Swartz
Parution	06/12/2001
Nb. de pages	158
Format	15,8 x 22,4
Couverture	Relié
Poids	367g
Intérieur	Noir et Blanc
EAN13	9789810242398