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Dimensions of level sets of generic continuous functions and generic H\"older functions defined on a fractal $F$ encode information about the geometry, ``the thickness" of $F$. While in the continuous case this quantity is related to a reasonably tam
Externí odkaz:
http://arxiv.org/abs/2312.04659
Hausdorff dimensions of level sets of generic continuous functions defined on fractals can give information about the "thickness/narrow cross-sections'' of a "network" corresponding to a fractal set, $F$. This lead to the definition of the topologica
Externí odkaz:
http://arxiv.org/abs/2111.06724
Publikováno v:
Journal of Mathematical Analysis and Applications Volume 516, Issue 2, 15 December 2022, 126543
Hausdorff dimensions of level sets of generic continuous functions defined on fractals were considered in two papers by R. Balka, Z. Buczolich and M. Elekes. In those papers the topological Hausdorff dimension of fractals was defined. In this paper w
Externí odkaz:
http://arxiv.org/abs/2110.04515
Publikováno v:
In Technological Forecasting & Social Change April 2024 201
In this paper we give an example of a closed, strongly one-sided dense set which is not of uniform density type. We also show that there is a set of uniform density type which is not of strong uniform density type.
Comment: Revised version after
Comment: Revised version after
Externí odkaz:
http://arxiv.org/abs/2101.09471
We denote the local ``little" Lipschitz constant of a function $f: {{\mathbb R}}\to { {\mathbb R}}$ by $ {\mathrm{lip}}f$. In this paper we settle the following question: For which sets $E {\subset} { {\mathbb R}}$ is it possible to find a continuous
Externí odkaz:
http://arxiv.org/abs/2001.05261
We denote the local "little" and "big" Lipschitz functions of a function $f: {{\mathbb R}}\to {{\mathbb R}}$ by $ {\mathrm {lip}}f$ and $ {\mathrm {Lip}}f$. In this paper we continue our research concerning the following question. Given a set $E {\su
Externí odkaz:
http://arxiv.org/abs/1907.00823
Given a continuous function $f: {{\mathbb R}}\to {{\mathbb R}}$ we denote the so-called "big Lip" and "little lip" functions by $ {{\mathrm {Lip}}} f$ and $ {{\mathrm {lip}}} f$ respectively}. In this paper we are interested in the following question
Externí odkaz:
http://arxiv.org/abs/1905.11081
Suppose $\Lambda$ is a discrete infinite set of nonnegative real numbers. We say that $ {\Lambda}$ is type $1$ if the series $s(x)=\sum_{\lambda\in\Lambda}f(x+\lambda)$ satisfies a zero-one law. This means that for any non-negative measurable $f: {{\
Externí odkaz:
http://arxiv.org/abs/1805.12419
Suppose $\Lambda$ is a discrete infinite set of nonnegative real numbers. We say that $ {\Lambda}$ is type $2$ if the series $s(x)=\sum_{\lambda\in\Lambda}f(x+\lambda)$ does not satisfy a zero-one law. This means that we can find a non-negative measu
Externí odkaz:
http://arxiv.org/abs/1804.10408