Geodesic
A Distribution Function of Cantor-Vitali Type
Canadian mathematical bulletin, Tome 7 (1964) no. 1, pp. 65-75

Voir la notice de l'article provenant de la source Cambridge University Press

In his 1922 article [l] on functions of bounded variation, Vitali gave a method for constructing monotone non-absolutely continuous functions, generalizing ideas from the ternary set introduced in another connection by Cantor. In [2], Hille and Tamarkin gave a full account of the "middle-third" function, showing it to be a singular distribution function, and finding its characteristic function. In [3], Evans obtained a generalization of the middle - third function by discarding middle intervals of length other than one-third, and obtained algorithms by which the moments of his function could be calculated. Invarious papers, among them [4], Wintner studied infinite convolutions of symmetric Bernoulli distributions, finding a great variety of distributions whose characteristic functions were of the form 
Sumner, D. B. A Distribution Function of Cantor-Vitali Type. Canadian mathematical bulletin, Tome 7 (1964) no. 1, pp. 65-75. doi: 10.4153/CMB-1964-009-6
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[1] 1. Vitali, G., Analisi delle funzioni a varia zione limitata. Rend, del Cire. Mat. di Palermo, Vol. 46 (1922), 388–408. Google Scholar

[2] 2. Hille, E. and Tamarkin, J. D., Remarks on a known example of a monotone continuous function. Amer. Math. Monthly, Vol. XXXVI (1929), No. 5, 255–264. Google Scholar

[3] 3. Evans, G. C., Calculation of moments for a Cantor-Vitali function, Herbert Ellsworth Slought Memorial Paper No. 6. Supp. Amer. Math. Monthly 64 (1957), No. 8, 22–27. Google Scholar

[4] 4. Jessen, B. and Wintner, A., Distribution functions and the Riemann Zeta function. Trans. Amer. Math. Soc., Vol. 38 (1935), 48–88. Google Scholar

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