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Differentiation Theory over Infinite-Dimensional Banach Spaces

ASCI, CLAUDIO
2016
  • journal article

Periodico
JOURNAL OF MATHEMATICS
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.
DOI
10.1155/2016/2619087
WOS
WOS:000390452900001
Archivio
http://hdl.handle.net/11368/2888977
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85014069060
https://www.hindawi.com/journals/jmath/2016/2619087/abs
Diritti
open access
FVG url
https://arts.units.it/bitstream/11368/2888977/1/2619087.pdf
Soggetti
  • Infinite product meas...

  • generalized Lebesgue ...

  • infinite-dimensional ...

  • change of variables' ...

Web of Science© citazioni
2
Data di acquisizione
Mar 20, 2024
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