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Symmetrically approximately continuous functions, consistent density theorems, and Fubini type inequalities
Author(s):
P.
D.
Humke;
M.
Laczkovich
Journal:
Trans. Amer. Math. Soc.
357
(2005),
31-44.
MSC (2000):
Primary 03E35;
Secondary 28A20, 26A03
Posted:
August 19, 2004
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Abstract:
Using the continuum hypothesis, Sierpinski constructed a nonmeasurable function  such that  is countable for every  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.
References:
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Additional Information:
P.
D.
Humke
Affiliation:
Department of Mathematics, Washington and Lee University, Lexington, Virginia 24450 -- and -- Department of Mathematics, St. Olaf College, Northfield, Minnesota 55057
Email:
humke@stolaf.edu
M.
Laczkovich
Affiliation:
Department of Analysis, Eötvös Loránd University, Budapest, Pázmány Péter sétány 1/C, 1117 Hungary -- and -- Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England
Email:
laczk@cs.elte.hu
DOI:
10.1090/S0002-9947-04-03682-7
PII:
S 0002-9947(04)03682-7
Keywords:
Fubini,
symmetrically approximately continuous,
covering number,
shrinking number
Received by editor(s):
March 10, 2003
Posted:
August 19, 2004
Additional Notes:
The second author's research was supported by the Hungarian National Foundation for Scientific Research Grant No. T032042.
Copyright of article:
Copyright
2004,
American Mathematical Society
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