Let Ω be an open subset of Rn, n >1, and let X be a Banach space. We prove that α-absolutely continuous functions f: Ω →X are continuous and differentiable (in some sense) almost everywhere in Ω.
Bongiorno, D. (2017). Absolutely continuous functions with values in a Banach space. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 451(Issue 2, 15 July 2017), 1216-1223 [10.1016/j.jmaa.2017.02.067].
Absolutely continuous functions with values in a Banach space
BONGIORNO, Donatella
2017-01-01
Abstract
Let Ω be an open subset of Rn, n >1, and let X be a Banach space. We prove that α-absolutely continuous functions f: Ω →X are continuous and differentiable (in some sense) almost everywhere in Ω.
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