Definition Measure_measure_function {Omega: Type} {sigma: SigmaAlgebra Omega} (m: Measure Omega): measurable_set Omega -> R := measure_function _ m.Definition GeneratedMeasure {A B} {sA: SigmaAlgebra A} {sB: SigmaAlgebra B} (f: MeasurableFunction A B) (mA: Measure A): Measure B.

Lemma GeneratedMeasure_spec: forall {A B} {sA: SigmaAlgebra A} {sB: SigmaAlgebra B} (f: MeasurableFunction A B) (mA: Measure A) (PB: measurable_set B), mA (PreImage_MSet f PB) = (GeneratedMeasure f mA) PB.