In some contexts the concept of "stopping time" is defined by requiring only that the occurrence or non-occurrence of the event τ = "t" is probabilistically independent of "X"t + 1, "X"t + 2, ... but not that it is completely determined by the history of the process up to time "t". That is a weaker condition than the one appearing in the paragraph above, but is strong enough to serve in some of the proofs in which stopping times are used.