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Measurable almost periodic functions

Published online by Cambridge University Press:  26 February 2010

H. Kestelman
H. Kestelman
Affiliation:
University College, London.
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Extract

A complex-valued function ƒ is said by W. Maak [1] to be almost periodic (a.p.) on Rn if for every positive number ε there is a decomposition of Rn into a finite number of sets S such that

for all h in Rn and all pairs x, y belonging to the same S. This definition is equivalent to that of Bohr when ƒ is continuous.

Type
Research Article
Information
Mathematika , Volume 3 , Issue 2 , December 1956 , pp. 140 - 143
Copyright
Copyright © University College London 1956

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References

1.Maak, W., Fastperiodische Funktionen (Springer, Berlin, 1950).CrossRefGoogle Scholar
2.Ursell, H. D., “Normality and almost periodic functions”, Journal London Math. Soc., 4 (1929), 123–127.CrossRefGoogle Scholar
3.Steinhaus, H., “Sur les distances …”, Fundamenta Math., 1 (1920), 93–104.CrossRefGoogle Scholar