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 spaces; infinite-dimensional differentiation theory; (m,δ)-general functions; change 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 forany strictly positive integer $k$, the Banach space $E_{I}$ of the boundedreal 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 thedifferentiation theory over $E_{I}$. The main result of our paper is a changeof variables' formula for the integration of the measurable real functions on$\left( \mathbf{R}^{I},\mathcal{B}^{(I)}\right)$. This change of variablesis defined by some functions over an open subset of $E_{J}$, with values on$E_{I}$, called $\left( m,\sigma\right)$-general, with properties thatgeneralize 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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