On the weak law of large numbers and the generalized elementary renewal theorem

@article{Smith1967OnTW,
title={On the weak law of large numbers and the generalized elementary renewal theorem},
author={W. L. Smith},
journal={Pacific Journal of Mathematics},
year={1967},
volume={22},
pages={171-188}
}

SUMMARY Much use is made of the fact that a necessary and sufficient condition for A Generalized Elementary Renewal Theorem (GERT) gives conditions such that, in which case (ex l + ",+ (~Xn)/n necessarily tends to J..L as n-> 00 , Finally, an example shows that (*) can hold while the WLLN fails to hold.