Geodesic
A Condition of Halo Type for the Differentiation of Classes of Integrals
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1015-1023

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

We shall consider a space S, a σ-algebra M of subsets of S, a measure μ defined on M, and the μ-integrals of certain μ-integrable functions f. To each point x of a certain set E of S we associate certain ones of the sets V ∈ M and form the quotients ∫ vf(x)dμ(x)/μ(V) for each such set V. In case these quotients tend to f(x) as the sets V converge to x in accordance with a definition we adopt in §2, then we say that the integral of f is differentiable or derivable at x. It is of interest to assert conditions that ensure the differentiability of a given integral or class of integrals at μ-almost all points of E. 
Jr., C. A. Hayes. A Condition of Halo Type for the Differentiation of Classes of Integrals. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1015-1023. doi: 10.4153/CJM-1966-102-0
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