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Mycielski-Regular Measures

Let μ be a Radon probability measure on M, the d-dimensional Real Euclidean space (where d is a positive integer), and f a measurable function. Let P be the space of sequences whose coordinates are elements in M. Then, for any point x in M, define a function ƒn on M and P that looks at the first n terms of an element of P and evaluates f at the first of those n terms that minimizes the distance to x in M. The measures for which such sequences converge in measure to f for almost every sequence are called Mycielski-regular. We show that the self-similar measure generated by a finite family of contracting similitudes and which up to a constant is the Hausdorff measure in its dimension on an invariant set C is Mycielski-regular.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc84171
Date08 1900
CreatorsBass, Jeremiah Joseph
ContributorsMauldin, R. Daniel, Urbański, Mariusz, Allaart, Pieter C.
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
FormatText
RightsPublic, Bass, Jeremiah Joseph, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved.

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