 The probability distribution "forgets" about the particular probability space used to define formula_6 and only records the probabilities of various values of formula_6.Such a probability distribution can always be captured by its cumulative distribution function

and sometimes also using a probability density function, formula_44.In measure-theoretic terms, we use the random variable formula_6 to "push-forward" the measure formula_46 on formula_4 to a measure formula_44 on formula_49.