Abstract
Let $X_i \geq 0$ be i.i.d. random variables with $E(X_i) = \infty$. Then for suitable functions $\varphi$ we have $\overline{\varphi(X)}/\varphi(\bar{X}) \rightarrow 0$ a.s. We give some applications of this result.
Citation
Jeesen Chen. Herman Rubin. "A Note on the Behavior of Sample Statistics when the Population Mean is Infinite." Ann. Probab. 12 (1) 256 - 261, February, 1984. https://doi.org/10.1214/aop/1176993388
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