A strictly increasing, pure jump process with stationary, independent increments hits a single point $r > 0$ with probability 0. Adapting a method of proof, due to Carleson, we obtain a similar result for processes with exchangeable increments. This enables us to solve a regularity problem from game theory concerning probabilities of covering single points by randomly ordered intervals.
"On Covering Single Points by Randomly Ordered Intervals." Ann. Probab. 9 (3) 520 - 528, June, 1981. https://doi.org/10.1214/aop/1176994426