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Integration in infinite-dimensional spaces

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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© 1990 Springer-Verlag

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Henstock, R. (1990). Integration in infinite-dimensional spaces. In: Bullen, P.S., Lee, P.Y., Mawhin, J.L., Muldowney, P., Pfeffer, W.F. (eds) New Integrals. Lecture Notes in Mathematics, vol 1419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083099

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  • DOI: https://doi.org/10.1007/BFb0083099

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52322-2

  • Online ISBN: 978-3-540-46955-1

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