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.



Titolo: Integration over an Infinite-Dimensional Banach Space and Probabilistic Applications
Autori: 
ASCI, CLAUDIO
Data di pubblicazione: 2014
Rivista: 
INTERNATIONAL JOURNAL OF ANALYSIS  
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.
Handle: http://hdl.handle.net/11368/2788325
Digital Object Identifier (DOI): 10.1155/2014/404186
Appare nelle tipologie:1.1 Articolo in Rivista

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