적분개념의 발달 (리만적분에서 르베그적분으로의 이행을 중심으로) = Development of the Integral Concept (from Riemann to Lebesgue)

다국어 초록 (Multilingual Abstract)

In the 19th century Fourier and Dirichlet studied the expansion of "arbitrary" functions into the trigonometric series and this led to the development of the Riemann's definition of the integral. Riemann's integral was considered to be of the highest generality and was discussed intensively. As a result, some weak points were found but, at least at the beginning, these were not considered as the criticism of the Riemann's integral. But after Jordan introduced the theory of content and measure-theoretic approach to the concept of the integral, and after Borel developed the Jordan's theory of content to a theory of measure, Lebesgue joined these two concepts together and obtained a new theory of integral, now known as the "Lebesgue integral".

참고문헌 (Reference)

1 Fourier, J. B. I, "Théorie analytique de la chaleur"

2 Grabiner, Judith V, "The Origins of Cauchy's Rigorous Calculus" Dover 1981

3 Lebesgue, H, "Sur le developpement de la notion d'intégrale" 19 : 54-74, 1926

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5 Lebesgue, H, "Notices sur les travaux scientifiques de M. Henri Lebesgue, Toulouse: Privat, or Oeuvres Scientifiques 1" 97-175, 1922

6 Darboux, G, "Ḿemoire sur les fonctions discontinues, Annales sciéntifiques de l'Ecole Normale Supéreure, 2éme série, IV" 57-112, 1875

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9 Euler, L, "Institutiones calculi integralis" St. Petersburg 1768-1780,

10 Euler, L, "Institutiones calculi differentialis" St. Petersburg 1755-,

11 Grattan-Guiness, L, "From the Calculus to Set Theory, 1630-1910 : An Introductory History" Duckworth 1980

12 Jahnke, Hans N, "A History of Analysis" AMS 2003