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The Riemann conditions for integrability and their influence on the notion of measure. (Les conditions de Riemann pour l’intégrabilité et leur influence sur la naissance de la notion de mesure.) (Italian. French summary) Zbl 0852.28001
This paper analyzes the part devoted to integration of Riemann’s famous 1854 memoir. This is followed by an examination of the subsequent work of Hankel (1870, published 1882), Darboux (1875), Ascoli (1875), Smith (1875), Dini (1878), Volterra (1881), du Bois-Reymond (1875) and Harnack (1880). The role of all those papers in the birth of measure theory is studied in detail.
MSC:
28-03 History of measure and integration
01A55 History of mathematics in the 19th century
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