On the convergence of induced measures in variation
Дарья Евгеньевна Александрова, Vladimir Igorevich Bogachev, Andrey Yurievich Pilipenko · Sbornik Mathematics · 1999
Let , be measurable maps such that and in measure on a measurable set . Conditions ensuring that the images of Lebesgue measure on under the maps converge in variation to the image of under are presented. For example, one sufficient condition is the convergence of the to in a Sobolev space with and the inclusion . Similar results are obtained for maps between Riemannian manifolds and maps from infinite dimensional spaces.