Geodesic
Lebesgue measure in infinite dimension as an infinite-dimensional distribution
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 8, pp. 127-132.

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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 the white noise theory. 
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R. Léandre. Lebesgue measure in infinite dimension as an infinite-dimensional distribution. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 8, pp. 127-132. http://geodesic.mathdoc.fr/item/FPM_2007_13_8_a8/

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