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Absolute continuity of vector-valued self-affine measures

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Title: Absolute continuity of vector-valued self-affine measures
Authors: Deng, Qi-Rong1 dengfractal@126.com
Source: Journal of Mathematical Analysis & Applications. Jun2008, Vol. 342 Issue 2, p1250-1264. 15p.
Subjects: Absolute continuity, Boundary value problems, Measure theory, Vector analysis
Abstract: Abstract: This paper is devoted to the absolute continuity of (scalar-valued or vector-valued) self-affine measures and their properties on the boundary of an invariant set. We first extend the definition of WSC to self-affine IFS, and then obtain a necessary and sufficient condition for the vector-valued self-affine measures to be absolutely continuous with respect to the Lebesgue measure. In addition, we prove that, for any IFS and any invariant open set V, the corresponding (scalar-valued or vector-valued) invariant measure is supported either in V or in ∂V. [Copyright &y& Elsevier]
Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 31397483
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PubType: Academic Journal
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  Data: Absolute continuity of vector-valued self-affine measures
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  Data: <searchLink fieldCode="AR" term="%22Deng%2C+Qi-Rong%22">Deng, Qi-Rong</searchLink><relatesTo>1</relatesTo><i> dengfractal@126.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Jun2008, Vol. 342 Issue 2, p1250-1264. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Absolute+continuity%22">Absolute continuity</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Measure+theory%22">Measure theory</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+analysis%22">Vector analysis</searchLink>
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  Data: Abstract: This paper is devoted to the absolute continuity of (scalar-valued or vector-valued) self-affine measures and their properties on the boundary of an invariant set. We first extend the definition of WSC to self-affine IFS, and then obtain a necessary and sufficient condition for the vector-valued self-affine measures to be absolutely continuous with respect to the Lebesgue measure. In addition, we prove that, for any IFS and any invariant open set V, the corresponding (scalar-valued or vector-valued) invariant measure is supported either in V or in ∂V. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jmaa.2007.12.041
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      – Code: eng
        Text: English
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        StartPage: 1250
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      – SubjectFull: Absolute continuity
        Type: general
      – SubjectFull: Boundary value problems
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      – SubjectFull: Measure theory
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      – SubjectFull: Vector analysis
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      – TitleFull: Absolute continuity of vector-valued self-affine measures
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              Text: Jun2008
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