Milloin joukon Lebesguen ja Hausdorffin mitat ovat yhtä suuria?

Tässä kirjoitelmassa tarkastelemme Lebesguen ja Hausdorffin mittojen suhdetta tai milloin ne ovat yhtä suuria. Tähän tarkasteluun tarvitsemme muun muassa n-ulotteisen pallon tilavuutta, Vitalin peitelausetta, tasaisesti jakautuneiden ja Borel-säännöllisten mittojen tarkastelua ja Steinerin symmetris...

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Main Author: Väätäinen, Juha
Other Authors: Matemaattis-luonnontieteellinen tiedekunta, Faculty of Sciences, Matematiikan ja tilastotieteen laitos, Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylän yliopisto
Format: Master's thesis
Language:fin
Published: 2012
Subjects:
Online Access: https://jyx.jyu.fi/handle/123456789/38624
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author Väätäinen, Juha
author2 Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Matematiikan ja tilastotieteen laitos Department of Mathematics and Statistics University of Jyväskylä Jyväskylän yliopisto
author_facet Väätäinen, Juha Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Matematiikan ja tilastotieteen laitos Department of Mathematics and Statistics University of Jyväskylä Jyväskylän yliopisto Väätäinen, Juha Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Matematiikan ja tilastotieteen laitos Department of Mathematics and Statistics University of Jyväskylä Jyväskylän yliopisto
author_sort Väätäinen, Juha
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description Tässä kirjoitelmassa tarkastelemme Lebesguen ja Hausdorffin mittojen suhdetta tai milloin ne ovat yhtä suuria. Tähän tarkasteluun tarvitsemme muun muassa n-ulotteisen pallon tilavuutta, Vitalin peitelausetta, tasaisesti jakautuneiden ja Borel-säännöllisten mittojen tarkastelua ja Steinerin symmetrisointia. Myös osoitamme, että Borelin joukot ovat Lebesgue- ja Hausdorff-mitallisia.
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spellingShingle Väätäinen, Juha Milloin joukon Lebesguen ja Hausdorffin mitat ovat yhtä suuria? Hausdorff Lebesgue Matematiikka Mathematics 4041 mitat matematiikka
title Milloin joukon Lebesguen ja Hausdorffin mitat ovat yhtä suuria?
title_full Milloin joukon Lebesguen ja Hausdorffin mitat ovat yhtä suuria?
title_fullStr Milloin joukon Lebesguen ja Hausdorffin mitat ovat yhtä suuria? Milloin joukon Lebesguen ja Hausdorffin mitat ovat yhtä suuria?
title_full_unstemmed Milloin joukon Lebesguen ja Hausdorffin mitat ovat yhtä suuria? Milloin joukon Lebesguen ja Hausdorffin mitat ovat yhtä suuria?
title_short Milloin joukon Lebesguen ja Hausdorffin mitat ovat yhtä suuria?
title_sort milloin joukon lebesguen ja hausdorffin mitat ovat yhtä suuria
title_txtP Milloin joukon Lebesguen ja Hausdorffin mitat ovat yhtä suuria?
topic Hausdorff Lebesgue Matematiikka Mathematics 4041 mitat matematiikka
topic_facet 4041 Hausdorff Lebesgue Matematiikka Mathematics matematiikka mitat
url https://jyx.jyu.fi/handle/123456789/38624 http://www.urn.fi/URN:NBN:fi:jyu-201209242501
work_keys_str_mv AT väätäinenjuha milloinjoukonlebesguenjahausdorffinmitatovatyhtäsuuria