This is a preview of subscription content, log in via an institution to check access.
References
Aczél, J.,Lectures on functional equations and their applications. Academic Press, New York-London, 1966.
Alexiewicz, A. etOrlicz, W.,Remarque sur l'équation fonctionnelle f(x+y)=f(x)+f(y). Fund. Math.33 (1945), 314–315.
Banach, S.,Sur l'équation fonctionnelle f(x+y)=f(x)+f(y). Fund. Math.1 (1920), 123–124.
Figiel, T. (Polish),The functional equation f(x+y)=f(x)+f(y). Wiadom. Mat. (2)11 (1969), 15–18.
Fréchet, M.,Pri la funkcia equacio f(x+y)=f(x)+f(y). Enseignement Math.15 (1913), 390–393.
Halmos, P.,Measure theory. Van Nostrand Reinhold Co., New York, 1950.
Jones, F. B.,Measure and other properties of a Hamel basis. Bull. Amer. Math. Soc.48 (1942), 472–481.
Kestelman, H.,On the functional equation f(x+y)=f(x)+f(y). Fund. Math.34 (1947), 144–147.
Kuczma, M. E. andKuczma, M.,An elementary proof and an extension of a theorem of Steinhaus. Glasnik Mat. Ser. III (26)6 (1971), 11–18.
Kuratowski, K.,Topologie. Vol. I. Monografie Matematyczne, Tom 20. Polish Scientific Publishers, Warszawa, 1958.
Ostrowski, A.,Über die Funktionalgleichung der Exponentialfunktion und verwandte Funktionalgleichungen. Jber. Deutsch. Math.-Verein.38 (1929), 54–62.
Sierpiński, W.,Sur la question de la mesurabilité de la base de M. Hamel. Fund. Math.1 (1920), 105–111.
Sierpiński, W.,Sur l'équation fonctionnelle f(x+y)=f(x)+f(y). Fund. Math.1 (1920), 116–122.
Sierpiński, W.,Sur les fonctions convexes mesurables. Fund. Math.1 (1920), 125–128.
Steinhaus, H.,Sur les distances des points dans les ensembles de mesure positive. Fund. Math.1 (1920), 93–104.
Zaanen, A. C.,Integration. North-Holland Publishing Co., Amsterdam, 1967.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kuczma, M., Smítal, J. On measures connected with the Cauchy equation. Aeq. Math. 14, 421–428 (1976). https://doi.org/10.1007/BF01835991
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01835991