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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Autores principales:	Byars Allison, Camrud Evan, Harding Steven N., McCarty Sarah, Sullivan Keith, Weber Eric S.
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	fractal cantor set sampling interpolation normal numbers 94a20 28a80 26a30 11k16 11k55 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/2d8a80e751ca4e9283022a78bbeb291b
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spelling	oai:doaj.org-article:2d8a80e751ca4e9283022a78bbeb291b2021-12-05T14:10:45ZSampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]2391-466110.1515/dema-2021-0010https://doaj.org/article/2d8a80e751ca4e9283022a78bbeb291b2021-05-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0010https://doaj.org/toc/2391-4661Cantor 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.Byars AllisonCamrud EvanHarding Steven N.McCarty SarahSullivan KeithWeber Eric S.De Gruyterarticlefractalcantor setsamplinginterpolationnormal numbers94a2028a8026a3011k1611k55MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 85-109 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	fractal cantor set sampling interpolation normal numbers 94a20 28a80 26a30 11k16 11k55 Mathematics QA1-939
spellingShingle	fractal cantor set sampling interpolation normal numbers 94a20 28a80 26a30 11k16 11k55 Mathematics QA1-939 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]
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.
format	article
author	Byars Allison Camrud Evan Harding Steven N. McCarty Sarah Sullivan Keith Weber Eric S.
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
publishDate	2021
url	https://doaj.org/article/2d8a80e751ca4e9283022a78bbeb291b
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Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]

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