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Lebesgue measure in infinite dimension as an infinite-dimensional distribution

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Abstract

Physicists deal with the formal Lebesgue measure on the space of smooth maps from one manifold to another. The aim of the present paper is to give two definitions of this measure as a distribution: using functional spaces of noncommutative geometry and those of white-noise theory.

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Authors and Affiliations

  1. Institut de Mathématiques, Université de Bourgogne, 21000, Dijon, France

    R. Léandre

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  1. R. Léandre
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Correspondence to R. Léandre.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 127–132, 2007.

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Léandre, R. Lebesgue measure in infinite dimension as an infinite-dimensional distribution. J Math Sci 159, 833–836 (2009). https://doi.org/10.1007/s10958-009-9475-2

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