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- W3100401878 abstract "We characterise purely $n$-unrectifiable subsets $S$ of a complete metric space $X$ with finite Hausdorff $n$-measure by studying arbitrarily small perturbations of elements of the set of all bounded 1-Lipschitz functions $fcolon X to mathbb R^m$ with respect to the supremum norm. In one such characterisation it is shown that, if $S$ has positive lower density almost everywhere, then the set of all $f$ with $mathcal H^n(f(S))=0$ is residual. Conversely, if $Esubset X$ is $n$-rectifiable with $mathcal H^n(E)>0$, the set of all $f$ with $mathcal H^n(f(E))>0$ is residual. These results provide a replacement for the Besicovitch-Federer projection theorem in arbitrary metric spaces, which is known to be false outside of Euclidean spaces." @default.
- W3100401878 created "2020-11-23" @default.
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- W3100401878 date "2020-01-01" @default.
- W3100401878 modified "2023-09-29" @default.
- W3100401878 title "Purely unrectifiable metric spaces and perturbations of Lipschitz functions" @default.
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- W3100401878 doi "https://doi.org/10.4310/acta.2020.v224.n1.a1" @default.
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