About: Characterization of Minkowski measurability in terms of surface area

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1016/j.jmaa.2012.10.059
Description	The r-parallel set to a set A in Euclidean space consists of all points with distance at most r from A. Recently, the asymptotic behaviour of volume and surface area of the parallel sets as r tends to 0 has been studied and some general results regarding their relations have been established. Here we complete the picture regarding the resulting notions of Minkowski content and S-content. In particular, we show that a set is Minkowski measurable if and only if it is S-measurable, i.e. if and only if its S-content is positive and finite, and that positivity and finiteness of the lower and upper Minkowski contents imply the same for the S-contents and vice versa. The results are formulated in the more general setting of Kneser functions. Furthermore, the relations between Minkowski and S-contents are studied for more general gauge functions. The results are applied to simplify the proof of the Modified Weyl-Berry conjecture in dimension one. The r-parallel set to a set A in Euclidean space consists of all points with distance at most r from A. Recently, the asymptotic behaviour of volume and surface area of the parallel sets as r tends to 0 has been studied and some general results regarding their relations have been established. Here we complete the picture regarding the resulting notions of Minkowski content and S-content. In particular, we show that a set is Minkowski measurable if and only if it is S-measurable, i.e. if and only if its S-content is positive and finite, and that positivity and finiteness of the lower and upper Minkowski contents imply the same for the S-contents and vice versa. The results are formulated in the more general setting of Kneser functions. Furthermore, the relations between Minkowski and S-contents are studied for more general gauge functions. The results are applied to simplify the proof of the Modified Weyl-Berry conjecture in dimension one. (en)
Title	Characterization of Minkowski measurability in terms of surface area Characterization of Minkowski measurability in terms of surface area (en)
skos:prefLabel	Characterization of Minkowski measurability in terms of surface area Characterization of Minkowski measurability in terms of surface area (en)
skos:notation	RIV/00216208:11320/13:10140149!RIV14-GA0-11320___
http://linked.open...avai/predkladatel	Matematicko-fyzikální fakulta
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GCP201/10/J039)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Rataj, Jan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	65085
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/13:10140149
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Kneser function; Gauge function; Minkowski dimension; Minkowski content; Surface area; Parallel set (en)
http://linked.open.../riv/klicoveSlovo	Kneser function Minkowski content Gauge function Minkowski dimension Parallel set Surface area
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[E803F26854F2]
http://linked.open...i/riv/nazevZdroje	Journal of Mathematical Analysis and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Curvature measures and integral geometry
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	400
http://linked.open...iv/tvurceVysledku	Rataj, Jan Winter, Steffen
http://linked.open...ain/vavai/riv/wos	000314672700012
issn	0022-247X
number of pages	13 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.jmaa.2012.10.059
http://localhost/t...ganizacniJednotka	11320

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