Semi-homogeneous functions

Authors:
Louis V. Quintas and Fred Supnick

Journal:
Proc. Amer. Math. Soc. **14** (1963), 620-625

MSC:
Primary 39.30

MathSciNet review:
0155117

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**[1]**The special case was first considered by the authors and the results announced in Abstract 577-8, Notices Amer. Math. Soc.**8**(1961), 51.**[2]**If and , then is the set of all constant functions. If ,*A*is not null, and on , then is the set of all functions which are constant on the cosets of and is an arbitrary constant.**[3]**Georg Hamel,*Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung: 𝑓(𝑥+𝑦)=𝑓(𝑥)+𝑓(𝑦)*, Math. Ann.**60**(1905), no. 3, 459–462 (German). MR**1511317**, 10.1007/BF01457624**[4]**By a decomposition of a set*X*we mean a disjoint family of subsets of*X*whose union is*X*.**[5]**Paul R. Halmos,*Measure Theory*, D. Van Nostrand Company, Inc., New York, N. Y., 1950. MR**0033869****[6]**H. Steinhaus,*A new property of G. Cantor's set*, Wektor**7**(1917). (Polish) See also, J. F. Randolph,*Distances between points of the Cantor set*, Amer. Math. Monthly**47**(1940), 549.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1963-0155117-3

Article copyright:
© Copyright 1963
American Mathematical Society