Superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions
We study the fractal properties (we find the Hausdorff-Bezikovich dimension and Hausdorff measure) of the spectrum of a random variable with independentn-adic (n≥2,n ∃N digits, the infinite set of which is fixed. We prove that the set of numbers of the segment [0, 1] that have no frequency of at lea...
Saved in:
| Date: | 1995 |
|---|---|
| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1995
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5492 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511721468198912 |
|---|---|
| author | Pratsiovytyi, M. V. Torbin, H. M. Працьовитий, М. В. Торбін, Г. М. |
| author_facet | Pratsiovytyi, M. V. Torbin, H. M. Працьовитий, М. В. Торбін, Г. М. |
| author_sort | Pratsiovytyi, M. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:11:49Z |
| description | We study the fractal properties (we find the Hausdorff-Bezikovich dimension and Hausdorff measure) of the spectrum of a random variable with independentn-adic (n≥2,n ∃N digits, the infinite set of which is fixed. We prove that the set of numbers of the segment [0, 1] that have no frequency of at least onen-adic digit is superfractal. |
| first_indexed | 2026-03-24T03:17:24Z |
| format | Article |
| fulltext |
0107
0108
0109
0110
0111
0112
0113
0114
0115
0116
0117
0118
0119
|
| id | umjimathkievua-article-5492 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:17:24Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/3a/d6984a2cee9562c255dda9e922bd883a.pdf |
| spelling | umjimathkievua-article-54922020-03-19T09:11:49Z Superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions Суперфрактальність множини чисел, які не мають частоти $n$-аднчних знаків, та фрактальні розподіли ймовірностей Pratsiovytyi, M. V. Torbin, H. M. Працьовитий, М. В. Торбін, Г. М. We study the fractal properties (we find the Hausdorff-Bezikovich dimension and Hausdorff measure) of the spectrum of a random variable with independentn-adic (n≥2,n ∃N digits, the infinite set of which is fixed. We prove that the set of numbers of the segment [0, 1] that have no frequency of at least onen-adic digit is superfractal. Вивчено фрактальні властивості (знайдено розмірність Хаусдорфа - Безнковнча і міру Хаусдорфа) спектра випадкової величини з незалежними $n$-адичннми ($n > 2, n є N$) знаками (цифрами), нескінченна множина яких фіксована. Доведено, що множина чисел відрізка $[0; 1],$ які не мають частоти хоча б одного $n$-аднчного знаку, є суперфрак галом. Institute of Mathematics, NAS of Ukraine 1995-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5492 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 7 (1995); 971–975 Український математичний журнал; Том 47 № 7 (1995); 971–975 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5492/7673 https://umj.imath.kiev.ua/index.php/umj/article/view/5492/7674 Copyright (c) 1995 Pratsiovytyi M. V.; Torbin H. M. |
| spellingShingle | Pratsiovytyi, M. V. Torbin, H. M. Працьовитий, М. В. Торбін, Г. М. Superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions |
| title | Superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions |
| title_alt | Суперфрактальність множини чисел, які не мають частоти $n$-аднчних знаків, та фрактальні розподіли ймовірностей |
| title_full | Superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions |
| title_fullStr | Superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions |
| title_full_unstemmed | Superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions |
| title_short | Superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions |
| title_sort | superfractality of the set of numbers having no frequency ofn-adic digits, and fractal probability distributions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5492 |
| work_keys_str_mv | AT pratsiovytyimv superfractalityofthesetofnumbershavingnofrequencyofnadicdigitsandfractalprobabilitydistributions AT torbinhm superfractalityofthesetofnumbershavingnofrequencyofnadicdigitsandfractalprobabilitydistributions AT pracʹovitijmv superfractalityofthesetofnumbershavingnofrequencyofnadicdigitsandfractalprobabilitydistributions AT torbíngm superfractalityofthesetofnumbershavingnofrequencyofnadicdigitsandfractalprobabilitydistributions AT pratsiovytyimv superfraktalʹnístʹmnožiničiselâkínemaûtʹčastotinadnčnihznakívtafraktalʹnírozpodílijmovírnostej AT torbinhm superfraktalʹnístʹmnožiničiselâkínemaûtʹčastotinadnčnihznakívtafraktalʹnírozpodílijmovírnostej AT pracʹovitijmv superfraktalʹnístʹmnožiničiselâkínemaûtʹčastotinadnčnihznakívtafraktalʹnírozpodílijmovírnostej AT torbíngm superfraktalʹnístʹmnožiničiselâkínemaûtʹčastotinadnčnihznakívtafraktalʹnírozpodílijmovírnostej |