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March 2016 An asymptotic extension of Moran construction in metric measure spaces
Daruhan Wu
Tsukuba J. Math. 39(2): 167-179 (March 2016). DOI: 10.21099/tkbjm/1461270054

Abstract

In this paper, we define asymptotically generalized Cantor sets in metric measure spaces by generalizing the notion of $\lambda$-similarity maps. We define the notion of $(\lambda, c, \nu)$-similarity maps, and extend the Moran theorem about the generalized Cantor set in $\mathbf{R}^d$ to this general setting. As an example, we construct generalized Cantor sets in Riemannian manifolds by using $(\lambda, c, \nu)$-similarity maps.

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Daruhan Wu. "An asymptotic extension of Moran construction in metric measure spaces." Tsukuba J. Math. 39 (2) 167 - 179, March 2016. https://doi.org/10.21099/tkbjm/1461270054

Information

Published: March 2016
First available in Project Euclid: 21 April 2016

MathSciNet: MR3490482
Digital Object Identifier: 10.21099/tkbjm/1461270054

Rights: Copyright © 2016 University of Tsukuba, Institute of Mathematics

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Vol.39 • No. 2 • March 2016
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