let formula_6 be a probability space, and let formula_7 be a random variable, defined as a borel-measurable function from formula_8 to its state space formula_9 then a regular conditional probability is defined as a function formula_10 called a "transition probability", where formula_11 is a valid probability measure (in its second argument) on formula_12 for all formula_13 and a measurable function in "e" (in its first argument) for all formula_14 such that for all formula_15 and all formula_16