Description

Book Synopsis
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.

Table of 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.

Introduction To Gauge Integrals

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    A Hardback by Charles W Swartz

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      Book details

      Publisher World Scientific Publishing Co Pte Ltd
      Published 1 June 2001
      ISBN-13 9789810242398
      978-9810242398
      ISBN-10 9810242395
      Also in:
      Calculus and mathematical analysis

      Description

      Book Synopsis
      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.

      Table of 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.

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