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Differentiation Theory over Infinite-Dimensional Banach Spaces

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  • Claudio Asci

Abstract

We study, for any positive integer and for any subset of , the Banach space of the bounded real sequences and a measure over that generalizes the -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 . This change of variables is defined by some infinite-dimensional functions with properties that generalize the analogous ones of the standard finite-dimensional diffeomorphisms.

Suggested Citation

  • Claudio Asci, 2016. "Differentiation Theory over Infinite-Dimensional Banach Spaces," Journal of Mathematics, Hindawi, vol. 2016, pages 1-16, December.
    • Handle: RePEc:hin:jjmath:2619087
    DOI: 10.1155/2016/2619087
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    References listed on IDEAS

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    1. Claudio Asci, 2014. "Integration over an Infinite-Dimensional Banach Space and Probabilistic Applications," International Journal of Analysis, Hindawi, vol. 2014, pages 1-10, June.
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    Cited by:

    1. Ali Jaballah & Fathi B. Saidi, 2017. "Orthogonal Symmetries and Reflections in Banach Spaces," Journal of Mathematics, Hindawi, vol. 2017, pages 1-9, June.

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