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

Allison Byars; Evan Camrud; Steven N. HardingSarah McCartyKeith SullivanEric S. Weber

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

机译：Sampling and interpolation of cumulative distribution functions of Cantor sets in 0, 1

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摘要

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.

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来源
《Demonstratio Mathematica》 |2021年第1期|85-109|共25页
作者
Allison Byars; Evan Camrud; Steven N. HardingSarah McCartyKeith SullivanEric S. Weber;
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作者单位

Department of Mathematics, University of Wisconsin Madison;

Department of Mathematics, Iowa State University;

Department of Mathematics, Milwaukee School of EngineeringDepartment of Mathematics, Concordia College;

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原文格式 PDF
正文语种英语
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关键词
fractal; Cantor set; sampling; interpolation; normal numbers;

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

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