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
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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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