The Journal of the Indian Mathematical Society

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A Diophantine Property of Some Summable Functions


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Let g(t) denote a function of the class L2 in O ≤ t ≤ I with period I. Let {fn (x) } (n = 1, 2,...) denote a sequence of real functions of x (a≤x<b). In a former paper [5] I proved that if fn (x) satisfies some general conditions, the relation

lim I/n Σ g(fn(x)) = ∫g(t)dt                (1).


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  • A Diophantine Property of Some Summable Functions

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Authors

J. F. Koksma
Amsterdam, Netherlands

Abstract


Let g(t) denote a function of the class L2 in O ≤ t ≤ I with period I. Let {fn (x) } (n = 1, 2,...) denote a sequence of real functions of x (a≤x<b). In a former paper [5] I proved that if fn (x) satisfies some general conditions, the relation

lim I/n Σ g(fn(x)) = ∫g(t)dt                (1).