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