Introduction to gauge integrals /

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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 un...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Swartz, Charles, 1938-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; River Edge, NJ : World Scientific, ©2001.
Temas:
Henstock-Kurzweil integral.
McShane integral.
Intégrale de Kurzweil-Henstock.
Intégrale de McShane.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Henstock-Kurzweil integral
McShane integral
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Introduction to the gauge or Henstock-Kurzweil integral
  • 2. Basic properties of the gauge integral
  • 3. Henstock's lemma and improper integrals
  • 4. The gauge integral over unbounded intervals
  • 5. Convergence theorems
  • 6. Integration over more general sets: Lebesgue measure
  • 7. The space of gauge integrable functions
  • 8. Multiple integrals and Fubini's theorem
  • 9. The McShane integral. 9.1. Definition and basic properties. 9.2. Convergence theorems. 9.3. Integrability of products and integration by parts. 9.4. More general convergence theorems. 9.5. The space of McShane integrable functions. 9.6. Multiple integrals and Fubini's theorem
  • 10. McShane integrability is equivalent to absolute Henstock-Kurzweil integrability.

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