BOREL, (FLIX-DOUARD-JUSTIN-) MILE

born Jan. 7, 1871, Saint-Affrique, Fr. died Feb. 3, 1956, Paris French mathematician who created the first effective theory of the measure of sets of points and who shared with Ren Baire and Henri Lebesgue of France in launching the modern theory of functions of a real variable. Appointed to the faculty of the cole Normale Suprieure, Paris, in 1896, Borel discovered the elementary proof of Picard's theorem. This sensational accomplishment set the stage for his formulation of a theory of integral functions and the distribution of their values, a topic that dominated the theory of complex functions for the next 30 years. As the creator of the first effective theory of the measure of sets of points, Borel helped launch the modern theory of functions of a real variable. Although he was not the first to define a conventional sum of a divergent series (a series of numbers that does not approach a certain number), he was the first to conceive and develop a systematic theory of such series (1899). In 1909 he was appointed to the chair of theory of functions created for him at the Sorbonne. He completed a series of papers on game theory (192127) and became the first to define games of strategy. Borel also served in the French Chamber of Deputies (192436) and as minister of the navy (192540). After his arrest and brief imprisonment under the Vichy regime in 1940, he returned to his native village and worked in the Resistance. For this work he was awarded the Resistance Medal (1945) to add to his Croix de Guerre (1918) and, later, the Grand Cross of the Legion of Honour (1950) and the first gold medal of the National Centre of Scientific Research (1955).