On p-adic cantor function

1991 ◽  
pp. 219-226
Author(s):  
Weixing Zheng
Keyword(s):  
Cantor Function

Distribution of values of classic singular Cantor function of random argument

2018 ◽  
Vol 26 (4) ◽  
pp. 193-200 ◽  
Author(s):  
Mykola Pratsiovytyi ◽  
Iryna Lysenko ◽  
Oksana Voitovska
Keyword(s):  
Random Variable ◽  
Absolutely Continuous ◽  
Cantor Function ◽  
Distribution Of Values

Abstract Let X be a random variable with independent ternary digits and let {y=F(x)} be a classic singular Cantor function. For the distribution of the random variable {Y=F(X)} , the Lebesgue structure (i.e., the content of discrete, absolutely continuous and singular components), the structure of its point and the continuous spectra are exhaustively studied.

A Note on the History of the Cantor Set and Cantor Function

1994 ◽  
Vol 67 (2) ◽  
pp. 136 ◽  
Author(s):  
Julian F. Fleron
Keyword(s):  
Cantor Set ◽  
Cantor Function ◽  
History Of

A Characterization of the Cantor Function

1991 ◽  
Vol 98 (3) ◽  
pp. 255-258 ◽  
Author(s):  
Donald R. Chalice
Keyword(s):  
Cantor Function

scholarly journals Characterization of the Local Growth of Two Cantor-Type Functions

2019 ◽  
Vol 3 (3) ◽  
pp. 45 ◽  
Author(s):  
Dimiter Prodanov
Keyword(s):  
Lebesgue Measure ◽  
Cantor Set ◽  
Positive Lebesgue Measure ◽  
Singular Function ◽  
Local Growth ◽  
Cantor Function ◽  
Physical Phenomena

The Cantor set and its homonymous function have been frequently utilized as examples for various physical phenomena occurring on discontinuous sets. This article characterizes the local growth of the Cantor’s singular function by means of its fractional velocity. It is demonstrated that the Cantor function has finite one-sided velocities, which are non-zero of the set of change of the function. In addition, a related singular function based on the Smith–Volterra–Cantor set is constructed. Its growth is characterized by one-sided derivatives. It is demonstrated that the continuity set of its derivative has a positive Lebesgue measure of 1/2.

Some Integrals Involving the Cantor Function

2009 ◽  
Vol 116 (3) ◽  
pp. 218-227 ◽  
Author(s):  
Russell A. Gordon
Keyword(s):  
Cantor Function
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