Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/27067
Title: Change of variables’ formula for the integration of the measurable real functions over infinite-dimensional Banach spaces
Authors: ASCI CLAUDIO
Keywords: Infinite-dimensional Banach spacesinfinite-dimensional differentiation theory(m,δ)-general functionschange of variables’ formula
Issue Date: 2019
Publisher: EUT Edizioni Università di Trieste
Source: Claudio Asci, "Change of variables’ formula for the integration of the measurable real functions over infinite-dimensional Banach spaces", in: "Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 51 (2019)", Trieste, EUT Edizioni Università di Trieste, 2019, pp. 61-103
Abstract: 
In this paper we study, for any subset\ $I$\ of $\mathbf{N}^{\ast}$ and for
any strictly positive integer $k$, the Banach space $E_{I}$ of the bounded
real sequences $\left\{ x_{n}\right\} _{n\in I}$, and a measure over
$\left( \mathbf{R}^{I},\mathcal{B}^{(I)}\right) $ that generalizes the
$k$-dimensional Lebesgue one. Moreover, we recall the main results about the
differentiation theory over $E_{I}$. The main result of our paper is a change
of variables' formula for the integration of the measurable real functions on
$\left( \mathbf{R}^{I},\mathcal{B}^{(I)}\right) $. This change of variables
is defined by some functions over an open subset of $E_{J}$, with values on
$E_{I}$, called $\left( m,\sigma\right) $-general, with properties that
generalize the analogous ones of the finite-dimensional diffeomorphisms.
Type: Article
URI: http://hdl.handle.net/10077/27067
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/27067
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.51 (2019)

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