We introduce a notion of Hilbertian n-volume in metric spaces with Besicovitch-type inequalities built-in into the definitions. The present Part 1 of the article is, for the most part, dedicated to the reformulation of known results in our terms with proofs being reduced to (almost) pure tautologies. If there is any novelty in the paper, this is in forging certain terminology which, ultimately, may turn useful in an Alexandrov kind of approach to singular spaces with positive scalar curvature [Gromov M., Plateau-hedra, Scalar Curvature and Dirac Billiards, in preparation].
@article{bwmeta1.element.doi-10_2478_s11533-011-0143-7,
author = {Misha Gromov},
title = {Hilbert volume in metric spaces. Part 1},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {371-400},
zbl = {1243.53077},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0143-7}
}
Misha Gromov. Hilbert volume in metric spaces. Part 1. Open Mathematics, Tome 10 (2012) pp. 371-400. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0143-7/
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