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2015•Proceedings of the Edinburgh Mathematical SocietyRequires access

Diagonals of Separately Absolutely Continuous Mappings Coincide with the Sums of Absolutely Convergent Series of Continuous Functions

Olena Karlova, Volodymyr V. Mykhaylyuk, Oleksandr Sobchuk

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Abstract

Abstract We prove that, for an interval X ⊆ ℝ and a normed space Z, diagonals of separately absolutely continuous mappings f : X2 → Z are exactly mappings g : X → Z, which are the sums of absolutely convergent series of continuous functions.

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What this paper is about

Abstract We prove that, for an interval X ⊆ ℝ and a normed space Z, diagonals of separately absolutely continuous mappings f : X2 → Z are exactly mappings g : X → Z, which are the sums of absolutely convergent series of continuous functions.

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Available abstract

Abstract We prove that, for an interval X ⊆ ℝ and a normed space Z, diagonals of separately absolutely continuous mappings f : X2 → Z are exactly mappings g : X → Z, which are the sums of absolutely convergent series of continuous functions.

Key concepts: Absolute continuity, Mathematics, Absolute convergence, Diagonal, Series (stratigraphy), Pure mathematics, Combinatorics, Mathematical analysis

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