Integration in infinite-dimensional spaces
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.
KeywordsFinite Order Finite Union Division Space Riemann Integration Partial Interval
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