A Perron-type integral of order two for Riesz-space-valued functions in terms of Peano derivatives is investigated. We give some fundamental properties of this integral and the integration by parts formula. In the present paper we deal with the second order Perron integral based on the Peano derivatives. This permits to obtain some known results under essentially weaker assumptions. Namely the hypotheses of boundedness of the derivatives of major and minor functions and super Dedekind completeness of the Riesz space can be dropped.
The Perron Integral of order Two in Riesz Spaces via Peano Derivatives
BOCCUTO, Antonio;SAMBUCINI, Anna Rita;
2009
Abstract
A Perron-type integral of order two for Riesz-space-valued functions in terms of Peano derivatives is investigated. We give some fundamental properties of this integral and the integration by parts formula. In the present paper we deal with the second order Perron integral based on the Peano derivatives. This permits to obtain some known results under essentially weaker assumptions. Namely the hypotheses of boundedness of the derivatives of major and minor functions and super Dedekind completeness of the Riesz space can be dropped.File in questo prodotto:
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