Article ID: CBB435431910

The Concept of Function at the Beginning of the 20th Century: A Historiographical Approach (2018)


The evolution of the concept of function at the beginning of the 20th century in France after the definitions by Dirichlet and Riemann and the introduction of several pathological functions is studied. Some young mathematicians of those years (Baire, known for his classification of discontinuous functions, Borel and Lebesgue famous for their new theories on measure and integration) made several attempts to propose a large class of functions as “accessible” objects. Their discussions, their purposes and polemics are reported often by their own words supported by a large bibliography. The contribution of some Italian mathematicians, as Vitali, is also underlined.  Some of such discussions are linked to the growth of measure and function theories, others will find mathematical answers in the modern theory of computability for real functions.

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Authors & Contributors
Mazliak, Laurent
Wang, Quanlai
González Redondo, Francisco A.
Rybnikov, K. A.
Barberousse, Anouk
Moore, Gregory H.
Revue d'Histoire des Mathématiques
Ziran Kexueshi Yanjiu (Studies in the History of Natural Sciences)
Historia Mathematica
Revue d'Histoire des Sciences
Journal Electronique d'Histoire des Probabilités et de la Statistique
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
Princeton University Press
Functions (mathematics)
Probability and statistics
Set theory
Borel, Felix Édouard Émile
Lebesgue, Henri
Fourier, Jean Baptiste Joseph
Poincaré, Jules Henri
Fréchet, Maurice René
Weierstrass, Karl Theodor
Time Periods
20th century, early
19th century
20th century
Institut Henri Poincaré
Université de Paris

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