Geodesic
On differentiation of integrals with respect to bases of convex sets.
Studia Mathematica, Tome 119 (1996) no. 2, pp. 99-108

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Differentiation of integrals of functions from the class $Lip(1,1)(I^2)$ with respect to the basis of convex sets is established. An estimate of the rate of differentiation is given. It is also shown that there exist functions in $Lip(1,1)(I^N)$, N ≥ 3, and $H^{ω}_{1}(I^2)$ with ω(δ)/δ → ∞ as δ → +0 whose integrals are not differentiated with respect to the bases of convex sets in the corresponding dimension. 
A. M. Stokolos. On differentiation of integrals with respect to bases of convex sets.. Studia Mathematica, Tome 119 (1996) no. 2, pp. 99-108. doi: 10.4064/sm-119-2-99-108
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