1. Introductory reminders about functions
Functions with bounded variations of a single variable were introduced in 1881 by the French mathematician C. Jordan (1838-1922). The Italian mathematician L. Tonelli (1885-1946) generalized the concept to continuous functions of several variables in 1926, followed by the Italian mathematician L. Cesari (1910-1990) replaced the continuity condition with the broader integrability condition in 1936, leading to the modern general concept.
Definition (indicator function). Let E be any non-empty set. The indicator function of a subset X of E is a function, denoted 1 E , defined on E and with values in {0,1} such that :
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