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Symmetrically approximately continuous functions, consistent density theorems, and Fubini type inequalities

Humke, PD; Laczkovich, M; (2005) Symmetrically approximately continuous functions, consistent density theorems, and Fubini type inequalities. T AM MATH SOC , 357 (1) 31 - 44. Green open access

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Abstract

Using the continuum hypothesis, Sierpinski constructed a non-measurable function f such that {h : f( x + h) not equal f(x - h)} is countable for every x: Clearly, such a function is symmetrically approximately continuous everywhere.Here we to show that Sierpinski's example cannot be constructed in ZFC. Moreover, we show it is consistent with ZFC that if a function is symmetrically approximately continuous almost everywhere, then it is measurable.

Type: Article
Title: Symmetrically approximately continuous functions, consistent density theorems, and Fubini type inequalities
Open access status: An open access version is available from UCL Discovery
Keywords: Fubini, symmetrically approximately continuous, covering number, shrinking number
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/8998
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