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

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 sch...

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Bibliographic Details
Main Authors:	Byars Allison, Camrud Evan, Harding Steven N., McCarty Sarah, Sullivan Keith, Weber Eric S.
Format:	Article
Language:	English
Published:	De Gruyter 2021-05-01
Series:	Demonstratio Mathematica
Subjects:	fractal cantor set sampling interpolation normal numbers 94a20 28a80 26a30 11k16 11k55
Online Access:	https://doi.org/10.1515/dema-2021-0010

id	doaj-2d8a80e751ca4e9283022a78bbeb291b
record_format	Article
spelling	doaj-2d8a80e751ca4e9283022a78bbeb291b2021-09-22T06:13:05ZengDe GruyterDemonstratio Mathematica2391-46612021-05-015418510910.1515/dema-2021-0010Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]Byars Allison0Camrud Evan1Harding Steven N.2McCarty Sarah3Sullivan Keith4Weber Eric S.5Department of Mathematics, University of Wisconsin Madison, 480 Lincoln Drive, Madison, WI 53706, USADepartment of Mathematics, Iowa State University, 411 Morrill Road, Ames, IA 50011, USADepartment of Mathematics, Milwaukee School of Engineering, 500 E. Kilbourn Ave., Milwaukee, WI 53202, USADepartment of Mathematics, Iowa State University, 411 Morrill Road, Ames, IA 50011, USADepartment of Mathematics, Concordia College, 901 8th St. S. Moorhead, MN 56562, USADepartment of Mathematics, Iowa State University, 411 Morrill Road, Ames, IA 50011, USACantor 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.https://doi.org/10.1515/dema-2021-0010fractalcantor setsamplinginterpolationnormal numbers94a2028a8026a3011k1611k55
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Byars Allison Camrud Evan Harding Steven N. McCarty Sarah Sullivan Keith Weber Eric S.
spellingShingle	Byars Allison Camrud Evan Harding Steven N. McCarty Sarah Sullivan Keith Weber Eric S. Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1] Demonstratio Mathematica fractal cantor set sampling interpolation normal numbers 94a20 28a80 26a30 11k16 11k55
author_facet	Byars Allison Camrud Evan Harding Steven N. McCarty Sarah Sullivan Keith Weber Eric S.
author_sort	Byars Allison
title	Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]
title_short	Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]
title_full	Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]
title_fullStr	Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]
title_full_unstemmed	Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]
title_sort	sampling and interpolation of cumulative distribution functions of cantor sets in [0, 1]
publisher	De Gruyter
series	Demonstratio Mathematica
issn	2391-4661
publishDate	2021-05-01
description	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.
topic	fractal cantor set sampling interpolation normal numbers 94a20 28a80 26a30 11k16 11k55
url	https://doi.org/10.1515/dema-2021-0010
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Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]

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