PROBABILISTIC PROOF OF THE MEAN-VALUE THEOREM FOR [0, 1]-VALUED MULTIPLICATIVE FUNCTIONS BY MEANS OF THE ADELIC FORMULATION
2023 年 77 巻 2 号 p. 355-366
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2023 年 77 巻 2 号 p. 355-366
A probabilistic proof by means of the adelic formulation is given to the classical mean-value theorem for [0, 1]-valued multiplicative arithmetical functions f. Then a more general mean-value theorem is derived for composite functions φ(f) of f with (semi-)continuous functions φ.
