MATHEMATICA BOHEMICA, Vol. 130, No. 1, pp. 49-62 (2005)

A scalar Volterra derivative for the $PoU$-integral

V. Marraffa

V. Marraffa, Department of Mathematics, University of Palermo, Via Archirafi, 34, 90123 Palermo, Italy, e-mail:

Abstract: A weak form of the Henstock Lemma for the $PoU$-integrable functions is given. This allows to prove the existence of a scalar Volterra derivative for the $PoU$-integral. Also the $PoU$-integrable functions are characterized by means of Pettis integrability and a condition involving finite pseudopartitions.

Keywords: Pettis integral, McShane integral, $PoU$ integral, Volterra derivative

Classification (MSC2000): 28B05, 46G10

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