branch for universe

[helm.git] / matita / contribs / dama / dama / classical_pointwise / sigma_algebra.ma

diff --git a/matita/contribs/dama/dama/classical_pointwise/sigma_algebra.ma b/matita/contribs/dama/dama/classical_pointwise/sigma_algebra.ma
new file mode 100644 (file)
index 0000000..580fe96
--- /dev/null
+++ b/matita/contribs/dama/dama/classical_pointwise/sigma_algebra.ma
@@ -0,0 +1,40 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+include "classical_pointwise/topology.ma".
+
+record is_sigma_algebra (X:Type) (A: set X) (M: set (set X)) : Prop ≝
+ { siga_subset: ∀B.B ∈ M → B ⊆ A;
+   siga_full: A ∈ M;
+   siga_compl: ∀B.B ∈ M → B \sup c ∈ M;
+   siga_enumerable_union:
+    ∀B:seq (set X).(∀i.(B \sub i) ∈ M) → (∪ \sub i B \sub i) ∈ M
+ }.
+
+record sigma_algebra : Type ≝
+ { siga_carrier:> Type;
+   siga_domain:> set siga_carrier;
+   M: set (set siga_carrier);
+   siga_is_sigma_algebra:> is_sigma_algebra ? siga_domain M
+ }.
+
+(*definition is_measurable_map ≝
+ λX:sigma_algebra.λY:topological_space.λf:X → Y.
+  ∀V. V ∈ O Y → f \sup -1 V ∈ M X.*)
+definition is_measurable_map ≝
+ λX:sigma_algebra.λY:topological_space.λf:X → Y.
+  ∀V. V ∈ O Y → inverse_image ? ? f V ∈ M X.
+