Matches in SemOpenAlex for { <https://semopenalex.org/work/W2953670785> ?p ?o ?g. }
Showing items 1 to 72 of
72
with 100 items per page.
- W2953670785 endingPage "284" @default.
- W2953670785 startingPage "263" @default.
- W2953670785 abstract "We prove that for any $1 leq k < n$ and $sleq 1$, the union of any nonempty $s$-Hausdorff dimensional family of $k$-dimensional affine subspaces of $mathbb R^n$ has Hausdorff dimension $k + s$. More generally, we show that for any $0 < alpha leq k$, if $B subset mathbb R^n$ and $E$ is a nonempty collection of $k$-dimensional affine subspaces of $mathbb R^n$ such that every $P in E$ intersects $B$ in a set of Hausdorff dimension at least $alpha$, then dim $B geq 2 alpha - k + mathrm {min}(mathrm {dim} E, 1)$, where dim denotes the Hausdorff dimension. As a consequence, we generalize the well-known Furstenberg-type estimate that every $alpha$-Furstenberg set has Hausdorff dimension at least $2 alpha$; we strengthen a theorem of Falconer and Mattila [5]; and we show that for any $0 leq k < n$, if a set $A subset mathbb R^n$ contains the $k$-skeleton of a rotated unit cube around every point of $mathbb R^n$, or if $A$ contains a $k$-dimensional affine subspace at a fixed positive distance from every point of $mathbb R^n$, then the Hausdorff dimension of $A$ is at least $k + 1$." @default.
- W2953670785 created "2019-07-12" @default.
- W2953670785 creator A5067471670 @default.
- W2953670785 creator A5086274692 @default.
- W2953670785 creator A5087874914 @default.
- W2953670785 date "2019-06-24" @default.
- W2953670785 modified "2023-10-17" @default.
- W2953670785 title "Hausdorff dimension of unions of affine subspaces and of Furstenberg-type sets" @default.
- W2953670785 doi "https://doi.org/10.4171/jfg/77" @default.
- W2953670785 hasPublicationYear "2019" @default.
- W2953670785 type Work @default.
- W2953670785 sameAs 2953670785 @default.
- W2953670785 citedByCount "7" @default.
- W2953670785 countsByYear W29536707852020 @default.
- W2953670785 countsByYear W29536707852021 @default.
- W2953670785 countsByYear W29536707852022 @default.
- W2953670785 countsByYear W29536707852023 @default.
- W2953670785 crossrefType "journal-article" @default.
- W2953670785 hasAuthorship W2953670785A5067471670 @default.
- W2953670785 hasAuthorship W2953670785A5086274692 @default.
- W2953670785 hasAuthorship W2953670785A5087874914 @default.
- W2953670785 hasBestOaLocation W29536707852 @default.
- W2953670785 hasConcept C114614502 @default.
- W2953670785 hasConcept C12362212 @default.
- W2953670785 hasConcept C134306372 @default.
- W2953670785 hasConcept C141898687 @default.
- W2953670785 hasConcept C173110770 @default.
- W2953670785 hasConcept C18903297 @default.
- W2953670785 hasConcept C191399826 @default.
- W2953670785 hasConcept C194198291 @default.
- W2953670785 hasConcept C202444582 @default.
- W2953670785 hasConcept C2777299769 @default.
- W2953670785 hasConcept C33676613 @default.
- W2953670785 hasConcept C33923547 @default.
- W2953670785 hasConcept C86803240 @default.
- W2953670785 hasConcept C92757383 @default.
- W2953670785 hasConceptScore W2953670785C114614502 @default.
- W2953670785 hasConceptScore W2953670785C12362212 @default.
- W2953670785 hasConceptScore W2953670785C134306372 @default.
- W2953670785 hasConceptScore W2953670785C141898687 @default.
- W2953670785 hasConceptScore W2953670785C173110770 @default.
- W2953670785 hasConceptScore W2953670785C18903297 @default.
- W2953670785 hasConceptScore W2953670785C191399826 @default.
- W2953670785 hasConceptScore W2953670785C194198291 @default.
- W2953670785 hasConceptScore W2953670785C202444582 @default.
- W2953670785 hasConceptScore W2953670785C2777299769 @default.
- W2953670785 hasConceptScore W2953670785C33676613 @default.
- W2953670785 hasConceptScore W2953670785C33923547 @default.
- W2953670785 hasConceptScore W2953670785C86803240 @default.
- W2953670785 hasConceptScore W2953670785C92757383 @default.
- W2953670785 hasIssue "3" @default.
- W2953670785 hasLocation W29536707851 @default.
- W2953670785 hasLocation W29536707852 @default.
- W2953670785 hasOpenAccess W2953670785 @default.
- W2953670785 hasPrimaryLocation W29536707851 @default.
- W2953670785 hasRelatedWork W144937262 @default.
- W2953670785 hasRelatedWork W2002679491 @default.
- W2953670785 hasRelatedWork W2069299945 @default.
- W2953670785 hasRelatedWork W2354912325 @default.
- W2953670785 hasRelatedWork W2577087656 @default.
- W2953670785 hasRelatedWork W2896057470 @default.
- W2953670785 hasRelatedWork W2953670785 @default.
- W2953670785 hasRelatedWork W2988187470 @default.
- W2953670785 hasRelatedWork W3120978378 @default.
- W2953670785 hasRelatedWork W3180428341 @default.
- W2953670785 hasVolume "6" @default.
- W2953670785 isParatext "false" @default.
- W2953670785 isRetracted "false" @default.
- W2953670785 magId "2953670785" @default.
- W2953670785 workType "article" @default.