In order to clarify the basic concepts involved in the definition of the Caccioppoli integral, the construction of a generating sequence is sketched, for functions nowhere differentiable; the definition of the Caccioppoli integral is then extended also to Banach-valued functions, together with a theorem of differentiation and a Vitali-type theorem. Moreover, it is shown that, in the scalar case, Riemann- Stieltjes integrability implies the existence of the Caccioppoli integral.
On the Caccioppoli Integral
CANDELORO, Domenico
2003
Abstract
In order to clarify the basic concepts involved in the definition of the Caccioppoli integral, the construction of a generating sequence is sketched, for functions nowhere differentiable; the definition of the Caccioppoli integral is then extended also to Banach-valued functions, together with a theorem of differentiation and a Vitali-type theorem. Moreover, it is shown that, in the scalar case, Riemann- Stieltjes integrability implies the existence of the Caccioppoli integral.File in questo prodotto:
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