In this paper we give a brief overview on the state of art of developments of Geometric Measure Theory in infinite-dimensional Banach spaces. The framework is given by an abstract Wiener space, that is a separable Banach space endowed with a centered Gaussian measure. The focus of the paper is on the theory of sets with finite perimeter and on their properties; this choice was motivated by the fact that most of the good properties of functions of bounded variation can be obtained, thanks to coarea formula, from the geometric properties of sets with finite perimeter.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc101-0-9,
author = {Michele Miranda Jr.},
title = {Some fine properties of sets with finite perimeter in Wiener spaces},
journal = {Banach Center Publications},
volume = {102},
year = {2014},
pages = {115-125},
zbl = {1296.28019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc101-0-9}
}
Michele Miranda Jr. Some fine properties of sets with finite perimeter in Wiener spaces. Banach Center Publications, Tome 102 (2014) pp. 115-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc101-0-9/