✦ LIBER ✦

On the convergence in variation for the images of measures under differentiable mappings

✍ Scribed by Daria Alexandrova; Vladimir Bogachev; Andrei Pilipenko

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 481 KB
Volume: 328
Category: Article
ISSN: 0764-4442
DOI: 10.1016/s0764-4442(99)80324-3

No coin nor oath required. For personal study only.

✦ Synopsis

Let F,, F : R" -R" be measurable mappings such that F, -+ F and a,,., F, -+ i),? F in measure on a measurable set E. We give conditions ensuring that the images of Lebesgue measure XII., on E under the mappings F, converge in the variation norm to the image of Xlk; under F. For example, a sufficient condition is that FJ -+ F in the Sobolev space I4 T1"'(Iwi'5 W") with y >_ n. and E c {det DF # O}. Analogous results are obtained for mappings between Riemannian manifolds and mappings from infinite-dimensional spaces. 0 Acadt?mie des SciencesElsevier, Paris Note pr&entke par Paul MALLIAC'IN.

📜 SIMILAR VOLUMES

On convergence in variation of one-dimen

On convergence in variation of one-dimensional image measures

✍ Yu. A. Davydov 📂 Article 📅 1995 🏛 Springer US 🌐 English ⚖ 388 KB

Weak convergence of probability measures

Weak convergence of probability measures in the spaces of continuously differentiable functions

✍ S. M. Prigarin 📂 Article 📅 1992 🏛 SP MAIK Nauka/Interperiodica 🌐 English ⚖ 282 KB

On necessary and sufficient conditions f

On necessary and sufficient conditions for convergence of probability measures in variation

✍ L.Ju. Vostrikova 📂 Article 📅 1984 🏛 Elsevier Science 🌐 English ⚖ 753 KB

Convergence under ×q of ×p Invariant Mea

Convergence under ×q of ×p Invariant Measures on the Circle

✍ A. Johnson; D.J. Rudolph 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 689 KB

On the Convergence of Coderivative of SA

On the Convergence of Coderivative of SAA Solution Mapping for a Parametric Stochastic Variational Inequality

✍ Jie Zhang; Li-wei Zhang; Li-ping Pang 📂 Article 📅 2011 🏛 Springer Netherlands 🌐 English ⚖ 599 KB

Remark on the convergence of the midpoin

Remark on the convergence of the midpoint method under mild differentiability conditions

✍ J.A. Ezquerro; M.A. Hernández; M.A. Salanova 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 190 KB

We establish a convergence theorem for the Midpoint method using a new system of rectu'rence relations. The purpose of this note is to relax its convergence conditions. We also give an example where our convergence theorem can be applied but other ones cannot.