We present an area formula for continuous mappings between metric spaces, under minimal regularity assumptions. In particular, we do not require any notion of differentiability. This is a consequence of a measure-theoretic notion of Jacobian, defined as the density of a suitable "pull-back measure". Finally, we give some applications and examples.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm124-2-11,
author = {Valentino Magnani},
title = {An area formula in metric spaces},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {275-283},
zbl = {1231.28007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm124-2-11}
}
Valentino Magnani. An area formula in metric spaces. Colloquium Mathematicae, Tome 122 (2011) pp. 275-283. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm124-2-11/