Characterization of Minkowski measurability in terms of surface area

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10140149" target="_blank" >RIV/00216208:11320/13:10140149 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jmaa.2012.10.059" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2012.10.059</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2012.10.059" target="_blank" >10.1016/j.jmaa.2012.10.059</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Characterization of Minkowski measurability in terms of surface area

Popis výsledku v původním jazyce

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 regardingtheir 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 itsS-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, therelations 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.

Název v anglickém jazyce

Characterization of Minkowski measurability in terms of surface area

Popis výsledku anglicky

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 regardingtheir 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 itsS-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, therelations 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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GCP201%2F10%2FJ039" target="_blank" >GCP201/10/J039: Míry křivosti a integrální geometrie</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

—

Svazek periodika

400

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

120-132

Kód UT WoS článku

000314672700012

EID výsledku v databázi Scopus

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