Geodesic
The Approximate Symmetric Integral
Canadian journal of mathematics, Tome 41 (1989) no. 3, pp. 508-555

Voir la notice de l'article provenant de la source Cambridge University Press

By a symmetric integral is understood an integral obtained from some kind of symmetric derivation process. Such integrals arise most naturally in the study of trigonometric series and in particular to handle the following problem. Suppose that a trigonometric series converges everywhere to a function À. It is known that this may occur without À being integrable in any of the more familiar senses so that the series may not be considered as a Fourier series of À; indeed Denjoy [4] has shown that if bnis a sequence of real numbers decreasing to zero but with +00 then the function À(x) = is not Denjoy-integrable. It is natural to ask then for an integration procedure that can be applied to À in order that the series be the Fourier series of À with respect to this integral. 
Preiss, D.; Thomson, B. S. The Approximate Symmetric Integral. Canadian journal of mathematics, Tome 41 (1989) no. 3, pp. 508-555. doi: 10.4153/CJM-1989-023-8
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