 Then an formula_82-valued random variable is a measurable function formula_84, which means that, for every subset formula_85, its preimage formula_86 where formula_87.This definition enables us to measure any subset formula_88 in the target space by looking at its preimage, which by assumption is measurable.In more intuitive terms, a member of formula_4 is a possible outcome, a member of formula_90 is a measurable subset of possible outcomes, the function formula_46 gives the probability of each such measurable subset, formula_15 represents the set of values that the random variable can take (such as the set of real numbers), and a member of formula_93 is a "well-behaved" (measurable) subset of formula_15 (those for which the probability may be determined).