Erratum to: Integration by Parts for Perron Type Integrals of Order 1 and 2 in Riesz Spaces

The proof of differentiability of the integral function I2 in [Boccuto-Sambucini-Skvortsov, Integration by Parts for Perron Type Integrals of Order 1 and 2 in Riesz Spaces, Theorem 7.9] is based on the sufficient condition for global differentiability; given in the paper Boccuto, A., Skvortsov, V.A.: Remark on the Maeda–Ogasawara–Vulikh representation theorem for Riesz spaces and applications to Differential Calculus. Acta Math. (Nitra) 9, 13–24 (2006). thes statement given in that paper is not justified in properly. In fact the following question seems to be open: if the “componentwise differentiability” in the complement of a meager set does imply global differentiability, where the involved “components” are taken according to the Maeda–Ogasawara–Vulikh representation theorem for Riesz spaces. To overcome this gap we present here a new proof of differentiability of the integral function I2.