Geodesic
A new quantitative analysis of some basic principles of the theory of functions of a real variable
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 26 (2001) no. 1.

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We define and study a new regularity requirement that one can put on sets of reals where a given function is to be continuous. The requirement is expressed in terms of number systems used in representing reals as strings of digits. We compare it with the classical requirement expressed in terms of the Lebesgue measure. 
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     title = {A new quantitative analysis of some basic principles of the theory of functions of a real variable},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
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S. Todorčević. A new quantitative analysis of some basic principles of the theory of functions of a real variable. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 26 (2001) no. 1. http://geodesic.mathdoc.fr/item/BASS_2001_26_1_a7/