On Tsirelson’s theorem about triple points for harmonic measure

Xavier Tolsa; Alexander Volberg

doi:10.1093/imrn/rnw345

On Tsirelson’s theorem about triple points for harmonic measure

Xavier Tolsa, Alexander Volberg

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

© The Author(s) 2017. Published by Oxford University Press. All rights reserved. A theorem of Tsirelson from 1997 asserts that given three disjoint domains in R n + 1 , the set of triple points belonging to the intersection of the three boundaries where the three corresponding harmonic measures are mutually absolutely continuous has null harmonic measure. The original proof by Tsirelson is based on the fine analysis of filtrations for Brownian and Walsh-Brownian motions and can not be translated into potential theory arguments. In the present article, we give a purely analytical proof of the same result.

Original language	English
Pages (from-to)	3671-3683
Journal	International Mathematics Research Notices
Volume	2018
Issue number	12
DOIs	https://doi.org/10.1093/imrn/rnw345
Publication status	Published - 1 Jun 2018

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title = "On Tsirelson{\textquoteright}s theorem about triple points for harmonic measure",

abstract = "{\textcopyright} The Author(s) 2017. Published by Oxford University Press. All rights reserved. A theorem of Tsirelson from 1997 asserts that given three disjoint domains in R n + 1 , the set of triple points belonging to the intersection of the three boundaries where the three corresponding harmonic measures are mutually absolutely continuous has null harmonic measure. The original proof by Tsirelson is based on the fine analysis of filtrations for Brownian and Walsh-Brownian motions and can not be translated into potential theory arguments. In the present article, we give a purely analytical proof of the same result.",

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AU - Volberg, Alexander

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N2 - © The Author(s) 2017. Published by Oxford University Press. All rights reserved. A theorem of Tsirelson from 1997 asserts that given three disjoint domains in R n + 1 , the set of triple points belonging to the intersection of the three boundaries where the three corresponding harmonic measures are mutually absolutely continuous has null harmonic measure. The original proof by Tsirelson is based on the fine analysis of filtrations for Brownian and Walsh-Brownian motions and can not be translated into potential theory arguments. In the present article, we give a purely analytical proof of the same result.

AB - © The Author(s) 2017. Published by Oxford University Press. All rights reserved. A theorem of Tsirelson from 1997 asserts that given three disjoint domains in R n + 1 , the set of triple points belonging to the intersection of the three boundaries where the three corresponding harmonic measures are mutually absolutely continuous has null harmonic measure. The original proof by Tsirelson is based on the fine analysis of filtrations for Brownian and Walsh-Brownian motions and can not be translated into potential theory arguments. In the present article, we give a purely analytical proof of the same result.

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DO - 10.1093/imrn/rnw345

M3 - Article

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EP - 3683

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

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ER -

On Tsirelson’s theorem about triple points for harmonic measure

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