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