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.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc84171 |
| Date | 08 1900 |
| Creators | Bass, Jeremiah Joseph |
| Contributors | Mauldin, R. Daniel, Urbański, Mariusz, Allaart, Pieter C. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | Text |
| Rights | Public, Bass, Jeremiah Joseph, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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