In this paper we study, for some subsets I of N^{∗}, the Banach space E of bounded real sequences {x_{n}}_{n∈I}. For any integer k, we introduce a measure over (E,B(E)) that generalizes the k-dimensional Lebesgue measure; consequently, also a theory of integration is defined. The main result of our paper is a change of variables formula for the integration.
Integration over an Infinite-Dimensional Banach Space and Probabilistic Applications
ASCI, CLAUDIO
2014-01-01
Abstract
In this paper we study, for some subsets I of N^{∗}, the Banach space E of bounded real sequences {x_{n}}_{n∈I}. For any integer k, we introduce a measure over (E,B(E)) that generalizes the k-dimensional Lebesgue measure; consequently, also a theory of integration is defined. The main result of our paper is a change of variables formula for the integration.File in questo prodotto:
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