## Doubly Uniform Complete Law of Large Numbers for Independent Point Processes

J. Math. Sci. Univ. Tokyo
Vol. 25 (2018), No. 2, Page 171-192.

Hattori, Tetsuya
Doubly Uniform Complete Law of Large Numbers for Independent Point Processes
We prove a law of large numbers in terms of uniform complete convergence of independent random variables taking values in functions of $2$ parameters which share similar monotonicity properties as the increments of monotone functions in the initial and the final time parameters. The assumptions for the main result are the Hölder continuity on the expectations as well as moment conditions, while the sample functions may contain jumps.