Another instructive example of a forcing poset is , where and is the collection of Borel subsets of having non-zero Lebesgue measure. The generic object associated with this forcing poset is a random real number . It can be shown that falls in every Borel subset of with measure 1, provided that the Borel subset is "described" in the original unexpanded universe (this can be formalized with the concept of Borel codes). Each forcing condition can be regarded as a random event with probability equal to its measure. Due to the ready intuition this example can provide, probabilistic language is sometimes used with other divergent forcing posets.
Another instructive example of a forcing poset is , where and is the collection of Borel subsets of having non-zero Lebesgue measure. The generic object associated with this forcing poset is a random real number . It can be shown that falls in every Borel subset of with measure 1 provided that the Borel subset is "described" in the original unexpanded universe (this can be formalized with the concept of Borel codes). Each forcing condition can be regarded as a random event with probability equal to its measure. Due to the ready intuition this example can provide, probabilistic language is sometimes used with other divergent forcing posets.