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

Part of: Real functions Functions of several variables Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  10 June 2015

Olena Karlova ,
Volodymyr Mykhaylyuk  and
Oleksandr Sobchuk
Olena Karlova
Affiliation:
Chernivtsi National University, Department of Mathematical Analysis, Kotsjubyns’koho 2, Chernivtsi 58012, Ukraine, ([email protected])
Volodymyr Mykhaylyuk
Affiliation:
Chernivtsi National University, Department of Mathematical Analysis, Kotsjubyns’koho 2, Chernivtsi 58012, Ukraine, ([email protected])
Oleksandr Sobchuk
Affiliation:
Chernivtsi National University, Department of Mathematical Analysis, Kotsjubyns’koho 2, Chernivtsi 58012, Ukraine, ([email protected])
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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.

Keywords

absolutely continuous functionsemi-continuityBaire-one mapping

MSC classification

Primary: 26B30: Absolutely continuous functions, functions of bounded variation
Secondary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) 54C10: Special maps on topological spaces (open, closed, perfect, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 435 - 444
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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