On almost continuous functions and peculiar points

Autor: Anna Loranty, Małgorzata Terepeta, Ryszard J. Pawlak
Rok vydání: 2018
Předmět:
Zdroj: European Journal of Mathematics. 5:106-115
ISSN: 2199-6768
2199-675X
DOI: 10.1007/s40879-018-0264-7
Popis: We introduce the concept of a peculiar point (of the first and second kind), which combines stability of functions around a given point on a large set in the sense of Lebesgue measure with strong chaos of a function (in the sense of its entropy value) around this point. We prove that almost continuity of a function is equivalent to the fact that in every $$\Gamma $$ -neighbourhood of this function one can find a continuous function having a peculiar point either of the first or second kind.
Databáze: OpenAIRE
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