Matches in SemOpenAlex for { <https://semopenalex.org/work/W2616537449> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W2616537449 abstract "We prove that for any singular measure $mu$ on $mathbb{R}^n$ it is possible to cover $mu$-almost every point with $n$ families of Lipschitz slabs of arbitrarily small total width. More precisely, up to a rotation, for every $delta>0$ there are $n$ countable families of $1$-Lipschitz functions ${f_i^1}_{iinmathbb{N}},ldots, {f_i^n}_{iinmathbb{N}},$ $f_i^j:{x_j=0}subsetmathbb{R}^ntomathbb{R}$, and $n$ sequences of positive real numbers ${varepsilon_i^1}_{iinmathbb{N}},ldots, {varepsilon_i^n}_{iinmathbb{N}}$ such that, denoting $hat x_j$ the orthogonal projection of the point $x$ onto ${x_j=0}$ and $$I_i^j:={x=(x_1,ldots,x_n)in mathbb{R}^n:f_i^j(hat x_j)-varepsilon_i^j< x_j< f_i^j(hat x_j)+varepsilon_i^j},$$ it holds $sum_{i,j}varepsilon_i^jleq delta$ and $mu(mathbb{R}^nsetminusbigcup_{i,j}I_i^j)=0.$ We apply this result to show that, if $mu$ is not absolutely continuous, it is possible to approximate the identity with a sequence $g_h$ of smooth equi-Lipschitz maps satisfying $$limsup_{htoinfty}int_{mathbb{R}^n}{rm{det}}(nabla g_h) dmu<mu(mathbb{R}^n).$$ From this, we deduce a simple proof of the fact that every top-dimensional Ambrosio-Kirchheim metric current in $mathbb{R}^n$ is a Federer-Fleming flat chain." @default.
- W2616537449 created "2017-05-26" @default.
- W2616537449 creator A5023679176 @default.
- W2616537449 date "2017-05-15" @default.
- W2616537449 modified "2023-09-27" @default.
- W2616537449 title "A covering theorem for singular measures in the Euclidean space" @default.
- W2616537449 cites W1487872891 @default.
- W2616537449 cites W2106387977 @default.
- W2616537449 cites W2330868067 @default.
- W2616537449 cites W2465207143 @default.
- W2616537449 cites W2964014490 @default.
- W2616537449 cites W650829231 @default.
- W2616537449 hasPublicationYear "2017" @default.
- W2616537449 type Work @default.
- W2616537449 sameAs 2616537449 @default.
- W2616537449 citedByCount "0" @default.
- W2616537449 crossrefType "posted-content" @default.
- W2616537449 hasAuthorship W2616537449A5023679176 @default.
- W2616537449 hasConcept C11413529 @default.
- W2616537449 hasConcept C114614502 @default.
- W2616537449 hasConcept C121332964 @default.
- W2616537449 hasConcept C127413603 @default.
- W2616537449 hasConcept C134306372 @default.
- W2616537449 hasConcept C22324862 @default.
- W2616537449 hasConcept C2779557605 @default.
- W2616537449 hasConcept C2780428219 @default.
- W2616537449 hasConcept C33923547 @default.
- W2616537449 hasConcept C54207081 @default.
- W2616537449 hasConcept C57493831 @default.
- W2616537449 hasConcept C62520636 @default.
- W2616537449 hasConcept C78519656 @default.
- W2616537449 hasConceptScore W2616537449C11413529 @default.
- W2616537449 hasConceptScore W2616537449C114614502 @default.
- W2616537449 hasConceptScore W2616537449C121332964 @default.
- W2616537449 hasConceptScore W2616537449C127413603 @default.
- W2616537449 hasConceptScore W2616537449C134306372 @default.
- W2616537449 hasConceptScore W2616537449C22324862 @default.
- W2616537449 hasConceptScore W2616537449C2779557605 @default.
- W2616537449 hasConceptScore W2616537449C2780428219 @default.
- W2616537449 hasConceptScore W2616537449C33923547 @default.
- W2616537449 hasConceptScore W2616537449C54207081 @default.
- W2616537449 hasConceptScore W2616537449C57493831 @default.
- W2616537449 hasConceptScore W2616537449C62520636 @default.
- W2616537449 hasConceptScore W2616537449C78519656 @default.
- W2616537449 hasLocation W26165374491 @default.
- W2616537449 hasOpenAccess W2616537449 @default.
- W2616537449 hasPrimaryLocation W26165374491 @default.
- W2616537449 hasRelatedWork W1968346858 @default.
- W2616537449 hasRelatedWork W2071792998 @default.
- W2616537449 hasRelatedWork W2219899869 @default.
- W2616537449 hasRelatedWork W2293327263 @default.
- W2616537449 hasRelatedWork W2304776585 @default.
- W2616537449 hasRelatedWork W2345785658 @default.
- W2616537449 hasRelatedWork W2370680011 @default.
- W2616537449 hasRelatedWork W2551704119 @default.
- W2616537449 hasRelatedWork W2552543005 @default.
- W2616537449 hasRelatedWork W2588572079 @default.
- W2616537449 hasRelatedWork W2619020576 @default.
- W2616537449 hasRelatedWork W2890050480 @default.
- W2616537449 hasRelatedWork W2947567073 @default.
- W2616537449 hasRelatedWork W2947933295 @default.
- W2616537449 hasRelatedWork W3100561307 @default.
- W2616537449 hasRelatedWork W3102976013 @default.
- W2616537449 hasRelatedWork W3109155526 @default.
- W2616537449 hasRelatedWork W3158495167 @default.
- W2616537449 hasRelatedWork W3197559772 @default.
- W2616537449 hasRelatedWork W55873533 @default.
- W2616537449 isParatext "false" @default.
- W2616537449 isRetracted "false" @default.
- W2616537449 magId "2616537449" @default.
- W2616537449 workType "article" @default.