In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in ...

Abstract. This is an attempt to give a systematic survey of properties of the famous Cantor ternary function.

This is an attempt to give a systematic survey of properties of the famous Cantor ternary function. Kеy words: Singular functions, Cantor function, Cantor set.

The Cantor function F(x) is the continuous but not absolutely continuous function on [0,1] which may be defined as follows. First, express x in ternary.

We already know that Cantor's set is infinite: it contains all endpoints of deleted intervals. There are only countably many such endpoints. We will show that ...

The Cantor distribution is the probability distribution whose cumulative distribution function is the Cantor function.

In these notes we will prove a few properties of the Cantor set and we will construct a pathological function 3 : [0,1] → [0,1] (the “Devil's staircase”) ...

13 дек. 2014 г. · the smallest integer n such that an=1 otherwise.

22 окт. 2024 г. · PDF | This is an attempt to give a systematic survey of properties of the famous Cantor ternary function. | Find, read and cite all the ...

The Cantor–Lebesgue function ϕ maps the Cantor set C, which has zero measure, to a set that has positive Lebesgue measure. Proof. If x /∈ C, then x belongs to ...