Geodesic
A scalar Volterra derivative for the PoU-integral
Mathematica Bohemica, Tome 130 (2005) no. 1, pp. 49-62

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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.
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.
DOI : 10.21136/MB.2005.134220
Classification : 28B05, 46G10
Keywords: Pettis integral; McShane integral; ${\mathrm PoU}$ integral; Volterra derivative 
Marraffa, V. A scalar Volterra derivative for the PoU-integral. Mathematica Bohemica, Tome 130 (2005) no. 1, pp. 49-62. doi: 10.21136/MB.2005.134220
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