  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
$1<s<\infty$, whose functions are proven to have the differentiability of
integrals associated to measurable sets classes in ${\bf 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 ${\bf R}^2 $, which is
continuous nowhere.
