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EnglishIn this paper we study, for any positive integer $k$ and for any subset\ $I$\ of $\QTR{bf}{N}^{\ast }$, the Banach space $E_{I}$ of the bounded real sequences $\left\{ x_{n}\right\} _{n\in I}$, and a measure over $\left( \QTR{bf}{R}^{I},\QTR{cal}{B}^{(I)}\right) $ that generalizes the $k$-dimensional Lebesgue one. Moreover, we expose a differentiation theory for the functions defined over this space. The main result of our paper is a change of variables' formula for the integration of the measurable real functions on $\left( \QTR{bf}{R}^{I},\QTR{cal}{B}^{(I)}\right) $. This change of variables is defined by some infinite-dimensional functions with properties that generalize the analogous ones of the standard finite-dimensional diffeomorphisms.
| Titolo: | Differentiation Theory over Infinite-Dimensional Banach Spaces |
| Autori: | |
| Data di pubblicazione: | 2016 |
| Stato di pubblicazione: | Pubblicato |
| Rivista: | |
| Abstract: | In this paper we study, for any positive integer $k$ and for any subset\ $I$\ of $\QTR{bf}{N}^{\ast }$, the Banach space $E_{I}$ of the bounded real sequences $\left\{ x_{n}\right\} _{n\in I}$, and a measure over $\left( \QTR{bf}{R}^{I},\QTR{cal}{B}^{(I)}\right) $ that generalizes the $k$-dimensional Lebesgue one. Moreover, we expose a differentiation theory for the functions defined over this space. The main result of our paper is a change of variables' formula for the integration of the measurable real functions on $\left( \QTR{bf}{R}^{I},\QTR{cal}{B}^{(I)}\right) $. This change of variables is defined by some infinite-dimensional functions with properties that generalize the analogous ones of the standard finite-dimensional diffeomorphisms. |
| Handle: | http://hdl.handle.net/11368/2888977 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1155/2016/2619087 |
| URL: | https://www.hindawi.com/journals/jmath/2016/2619087/abs |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| 2619087.pdf | Articolo principale | Documento in Versione Editoriale |  | Open Access Visualizza/Apri |
http://hdl.handle.net/11368/2888977
