A Diophantine Property of Some Summable Functions

Jump To References Section

Authors

  • Amsterdam ,NL

DOI:

https://doi.org/10.18311/jims/1951/17072

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).