Semihomogeneous functions
Authors:
Louis V. Quintas and Fred Supnick
Journal:
Proc. Amer. Math. Soc. 14 (1963), 620625
MSC:
Primary 39.30
MathSciNet review:
0155117
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References 
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Additional Information
 [1]
The special case was first considered by the authors and the results announced in Abstract 5778, 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, http://dx.doi.org/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
(11,504d)
 [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.
 [1]
 The special case was first considered by the authors and the results announced in Abstract 5778, 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]
 G. Hamil, Eine Basis aller Zahlen und die unstetige Lösungen der Funktionalgleichung , Math. Ann. 60 (1905), 459462. MR 1511317
 [4]
 By a decomposition of a set X we mean a disjoint family of subsets of X whose union is X.
 [5]
 P. R. Halmos, Measure theory, Van Nostrand, Princeton, N. J., 1950, Theorem B, p. 68. MR 0033869 (11:504d)
 [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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939196301551173
PII:
S 00029939(1963)01551173
Article copyright:
© Copyright 1963
American Mathematical Society
