Class ProbabilityMeasureFamily (Omega: Type) {SigFamily : SigmaAlgebraFamily Omega}: Type := {
  sub_measure: forall (P: Ensemble Omega | is_measurable_subspace P), @ProbabilityMeasure {o: Omega | proj1_sig P o} (sub_sigma_algebra P)
}.Class ProbabilityMeasureFamily (Omega: Type) {SigFamily : SigmaAlgebraFamily Omega}: Type := {
  sub_measure: forall (P: Ensemble Omega | is_measurable_subspace P), @ProbabilityMeasure {o: Omega | proj1_sig P o} (sub_sigma_algebra P)
}.Definition measurable_subspace: Type := {Omega: Ensemble U | is_measurable_subspace Omega}.Definition measurable_subspace_Ensemble: measurable_subspace -> Ensemble U := @proj1_sig _ _.Definition measurable_subspace_Prop: measurable_subspace -> U -> Prop := @proj1_sig _ _.Definition is_measurable_set (P: Ensemble U) (Omega: measurable_subspace) := @is_measurable_set {x: U | Omega x} (sub_sigma_algebra Omega) (sig_Set P Omega).

(* Specifications: *)
Lemma is_measurable_subspace_consi: forall (Omega Omega': measurable_subspace), Included Omega' Omega -> is_measurable_set Omega' Omega.