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Integration in infinite-dimensional spaces

  • Ralph Henstock
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1419)

Abstract

Three exact new proofs are given of vital results. The division space integral over infinite-dimensional product spaces can be defined using a bare minimum of conditions (Theorem 1). For certain absolute and non-absolute conditions of integrability, a real functional is constant almost everywhere if cylindrical of every finite order (Theorem 2). If the integration is absolute, the integral's value is in a sense the limit almost everywhere of the integrals over some sequences of finite-dimensional sets (Theorem 4).

This paper was written during the term of a two-year Leverhulme Trust Emeritus Fellowship award for the study of integration theory.

Keywords

Finite Order Finite Union Division Space Riemann Integration Partial Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Ralph Henstock
    • 1
  1. 1.University of UlsterColeraineIreland

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