IsisCB Explore

Article ID: CBB435431910

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

Biacino, Loredana (Author)

Transversal: International Journal for the Historiography of Science
Issue: 5
Pages: 171-192

URI: http://www.historiographyofscience.org/index.php/transversal/article/view/109

DOI: 10.24117/2526-2270.2018.i5.13

Outside Links

WorldCat

Google Scholar

JSTOR

Academia.edu

Historiography Mathematics Functions (mathematics) 20th century, early France Vitali, Giuseppe Borel, Felix Édouard Émile Lebesgue, Henri Baire, René Louis Dirichlet, Johann Peter Gustav Lejeune Riemann, Georg Friedrich Bernhard

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.

...More

Citation URI

http://data.isiscb.org/isis/citation/CBB435431910/

Citations Indexes

Similar Citations

Article Wang, Quanlai; (2008)
The Research on Emile Borel's Work Relative to Function Singularities (/isis/citation/CBB000933527/)

Article Maurey, Bernard; Tacchi, Jean-Pierre; (2013)
Sur le théorème de recouvrement de Vitali: L'apprivoisement des constructions ensemblistes infinies (/isis/citation/CBB001211055/)

Article Mazliak, Laurent; (2010)
Borel, Fréchet, Darmois: La découverte des statistiques par les probabilistes français (/isis/citation/CBB001024451/)

Article Siegmund-Schultze, Reinhard; (2009)
The Institute Henri Poincaré and Mathematics in France between the Wars (/isis/citation/CBB000954527/)

Book Volterra, Vito; Mazliak, Laurent; Tazzioli, Rossana; (2009)
Mathematicians at War: Volterra and His French Colleagues in World War I (/isis/citation/CBB001251203/)

Article Tinne Hoff Kjeldsen; Jesper Lützen; (2015)
Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics (/isis/citation/CBB766129464/)

Article Moore, Gregory H.; (2008)
The Emergence of Open Sets, Closed Sets, and Limit Points in Analysis and Topology (/isis/citation/CBB000950203/)

Article Enrico Rogora; (2021)
A Priority Claim of Henri Lebesgue against Leonida Tonelli (/isis/citation/CBB674062575/)

Book Gray, Jeremy; (2008)
Plato's Ghost: The Modernist Transformation of Mathematics (/isis/citation/CBB000950298/)

Article Duda, Roman; (2007)
Some Questions for the Study of History of Mathematics (/isis/citation/CBB001021438/)

Article Borovik, Alexandre; Katz, Mikhail G.; (2012)
Who Gave You the Cauchy-Weierstrass Tale? The Dual History of Rigorous Calculus (/isis/citation/CBB001252708/)

Article Wang, Quanlai; (2009)
The Research on Emile Borel's Work Relative to Theory of Zero Measure Set (/isis/citation/CBB000933758/)

Article Barberousse, Anouk; (2008)
La valeur de la connaissance approchée. L'épistémologie de l'approximation d'Émile Borel (/isis/citation/CBB000930660/)

Article Izabela Jóźwik; Lech Maligranda; Małgorzata Terepeta; (2019)
Stefan Kempisty (1892–1940) (/isis/citation/CBB716134567/)

Article Bru, Bernard; Bru, Marie France; Chung, Kai Lai; (2009)
Borel and the St. Petersburg Martingale (/isis/citation/CBB001021417/)

Article Durand, Antonin; Mazliak, Laurent; (2011)
Revisiting the Sources of Borel's Interest in Probability: Continued Fractions, Social Involvement, Volterra's Prolusione (/isis/citation/CBB001230538/)

Article Catellier, Rémi; Mazliak, Laurent; (2012)
The Emergence of French Probabilistic Statistics. Borel and the Institut Henri Poincaré around the 1920s (/isis/citation/CBB001211451/)

Article González Redondo, Francisco A.; (2002)
Daviet de Foncenex y Lazare Carnot: ¿Las raíces dimensionales de Fourier? Algunos comentarios a Martins, Grattan-Guinnes y Gillespie (/isis/citation/CBB000300774/)

Article Gispert, Hélène; Leloup, Juliette; (2009)
Des patrons des mathématiques en France dans l'entre-deux-guerres (/isis/citation/CBB000954522/)

Article Rybnikov, K. A.; (2003)
Iz istorii matematicheskoi teorii igr (/isis/citation/CBB000321063/)