Abstract
The behavior of (1/N)\(\sum _{n = 1}^N f\left( {S_n } \right)\) asN→∞ is considered, wheref is a bounded measurable function on (−∞, ∞) and (S n) =1/∞ n are the partial sums of a sequence of independent and identically distributed rondom variables.
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Meilijson, I. The average of the values of a function at random points. Israel J. Math. 15, 193–203 (1973). https://doi.org/10.1007/BF02764606
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DOI: https://doi.org/10.1007/BF02764606