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.