Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]-Reference-Cited by-同舟云学术

Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]

Published:2021-01-01 Issue:1 Volume:54 Page:85-109
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Byars Allison¹,Camrud Evan²,Harding Steven N.³,McCarty Sarah²,Sullivan Keith⁴,Weber Eric S.²

Affiliation:

1. Department of Mathematics, University of Wisconsin Madison, 480 Lincoln Drive , Madison , WI 53706 , USA

2. Department of Mathematics, Iowa State University, 411 Morrill Road , Ames , IA 50011 , USA

3. Department of Mathematics, Milwaukee School of Engineering, 500 E. Kilbourn Ave. , Milwaukee , WI 53202 , USA

4. Department of Mathematics, Concordia College, 901 8th St . S. Moorhead , MN 56562 , USA

Abstract

Abstract Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), constructed from the invariant Borel probability measure associated with their iterated function systems. Under appropriate assumptions, we identify sampling schemes of such CDFs, meaning that the underlying Cantor set can be reconstructed from sufficiently many samples of its CDF. To this end, we prove that two Cantor sets have almost-nowhere intersection with respect to their corresponding invariant measures.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2021-0010/pdf

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