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On differentiation of integrals with respect to bases of convex sets.

A. Stokolos (1996)

Studia Mathematica

Differentiation of integrals of functions from the class L i p ( 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 L i p ( 1 , 1 ) ( I N ) , N ≥ 3, and H 1 ω ( 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.

On the σ -finiteness of a variational measure

Diana Caponetti (2003)

Mathematica Bohemica

The σ -finiteness of a variational measure, generated by a real valued function, is proved whenever it is σ -finite on all Borel sets that are negligible with respect to a σ -finite variational measure generated by a continuous function.

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