Definition ConstantFunction {A B: Type} {sA: SigmaAlgebra A} {sB: SigmaAlgebra B} (b0: B): MeasurableFunction A B.Definition Indicator {A B: Type} {sA: SigmaAlgebra A} {sB: SigmaAlgebra B} (P: measurable_set A) (b0 b1: B): MeasurableFunction A B.

(* Specifications: *)
Lemma Indicator_True: forall {A B: Type} {sA: SigmaAlgebra A} {sB: SigmaAlgebra B} (P: measurable_set A) (b0 b1: B) (a: A), P a -> Indicator P b0 b1 a b1.
Lemma Indicator_False: forall {A B: Type} {sA: SigmaAlgebra A} {sB: SigmaAlgebra B} (P: measurable_set A) (b0 b1: B) (a: A), ~ P a -> Indicator P b0 b1 a b0.