One class of continuous locally complicated functions related to infinite-symbol $\Phi$-representation of numbers

One class of continuous locally complicated functions related to infinite-symbol $\Phi$-representation of numbers

In the paper, we introduce and study a massive class of continuous functions defined on the interval $(0;1)$ using a special encoding (representation) of the argument with an alphabet $ \mathbb{Z}=\{0,\pm 1, \pm 2,...\}$ and base $\tau=\frac{\sqrt{5}-1}{2}$: $\displaystyle x=b_{\alpha_1}+\sum\limits...

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Bibliographic Details
Main Authors: M. V. Pratsovytyi, O. M. Baranovskyi, O.I. Bondarenko, S.P. Ratushniak
Format: Article
Language:deu
Published: Ivan Franko National University of Lviv 2023-06-01
Series:Математичні Студії
Subjects:
$\phi$-representation; cylindrical sets; cantor-type function; quasi-cantor type function; nowhere monotonic function; continuous function of unbounded variation; lebesgue structure of a function; lebesgue structure of a probability measure
Online Access:http://matstud.org.ua/ojs/index.php/matstud/article/view/428
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http://matstud.org.ua/ojs/index.php/matstud/article/view/428

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