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No functions class for general measurable sets classes are known whose functions have the property of differentiability of integrals associated to such sets classes.In this paper, we give some subspaces of L s with 1 < s < ∞, whose functions are proven to have the differentiability of integrals associated to measurable sets classes in R n , this gives an answer to a question stated by Stein in his book Harmonic Analysis.We give also a example of some functions in these classes on R 2 , which is continuous nowhere.
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A 1971 study studied this question.
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