author hoelzl Fri, 16 Nov 2012 14:46:23 +0100 changeset 50101 a3bede207a04 parent 50100 9af8721ecd20 child 50103 3d89c38408cd
renamed prob_space to proj_prob_space as it clashed with Probability_Measure.prob_space
```--- a/src/HOL/Probability/Projective_Family.thy	Fri Nov 16 14:46:23 2012 +0100
+++ b/src/HOL/Probability/Projective_Family.thy	Fri Nov 16 14:46:23 2012 +0100
@@ -81,7 +81,7 @@
fixes I::"'i set" and P::"'i set \<Rightarrow> ('i \<Rightarrow> 'a) measure" and M::"('i \<Rightarrow> 'a measure)"
assumes projective: "\<And>J H X. J \<noteq> {} \<Longrightarrow> J \<subseteq> H \<Longrightarrow> H \<subseteq> I \<Longrightarrow> finite H \<Longrightarrow> X \<in> sets (PiM J M) \<Longrightarrow>
(P H) (prod_emb H M J X) = (P J) X"
-  assumes prob_space: "\<And>J. finite J \<Longrightarrow> prob_space (P J)"
+  assumes proj_prob_space: "\<And>J. finite J \<Longrightarrow> prob_space (P J)"
assumes proj_space: "\<And>J. finite J \<Longrightarrow> space (P J) = space (PiM J M)"
assumes proj_sets: "\<And>J. finite J \<Longrightarrow> sets (P J) = sets (PiM J M)"
begin
@@ -133,7 +133,7 @@
let ?\<Omega> = "(\<Pi>\<^isub>E k\<in>J. space (M k))"
show "Int_stable ?J"
by (rule Int_stable_PiE)
-  interpret prob_space "P J" using prob_space `finite J` by simp
+  interpret prob_space "P J" using proj_prob_space `finite J` by simp
show "emeasure ?P (?F _) \<noteq> \<infinity>" using assms `finite J` by (auto simp: emeasure_limP)
show "?J \<subseteq> Pow ?\<Omega>" by (auto simp: Pi_iff dest: sets_into_space)
show "sets (limP J M P) = sigma_sets ?\<Omega> ?J" "sets (P J) = sigma_sets ?\<Omega> ?J"
@@ -165,7 +165,7 @@
have "\<forall>i\<in>L. \<exists>x. x \<in> space (M i)"
proof
fix i assume "i \<in> L"
-    interpret prob_space "P {i}" using prob_space by simp
+    interpret prob_space "P {i}" using proj_prob_space by simp
from not_empty show "\<exists>x. x \<in> space (M i)" by (auto simp add: proj_space space_PiM)
qed
from bchoice[OF this]```
```--- a/src/HOL/Probability/Projective_Limit.thy	Fri Nov 16 14:46:23 2012 +0100
+++ b/src/HOL/Probability/Projective_Limit.thy	Fri Nov 16 14:46:23 2012 +0100
@@ -207,7 +207,7 @@
OF `I \<noteq> {}`, OF `I \<noteq> {}`])
fix A assume "A \<in> ?G"
with generatorE guess J X . note JX = this
-    interpret prob_space "P J" using prob_space[OF `finite J`] .
+    interpret prob_space "P J" using proj_prob_space[OF `finite J`] .
show "\<mu>G A \<noteq> \<infinity>" using JX by (simp add: limP_finite)
next
fix Z assume Z: "range Z \<subseteq> ?G" "decseq Z" "(\<Inter>i. Z i) = {}"
@@ -241,7 +241,7 @@
note [simp] = `\<And>n. finite (J n)`
from J  Z_emb have Z_eq: "\<And>n. Z n = emb I (J n) (B n)" "\<And>n. Z n \<in> ?G"
unfolding J_def B_def by (subst prod_emb_trans) (insert Z, auto)
-      interpret prob_space "P (J i)" for i using prob_space by simp
+      interpret prob_space "P (J i)" for i using proj_prob_space by simp
have "?a \<le> \<mu>G (Z 0)" by (auto intro: INF_lower)
also have "\<dots> < \<infinity>" using J by (auto simp: Z_eq \<mu>G_eq limP_finite proj_sets)
finally have "?a \<noteq> \<infinity>" by simp
@@ -636,13 +636,13 @@
show "emeasure (lim\<^isub>B I P) (space (lim\<^isub>B I P)) = 1"
proof cases
assume "I = {}"
-    interpret prob_space "P {}" using prob_space by simp
+    interpret prob_space "P {}" using proj_prob_space by simp
show ?thesis
by (simp add: space_PiM_empty limP_finite emeasure_space_1 `I = {}`)
next
assume "I \<noteq> {}"
then obtain i where "i \<in> I" by auto
-    interpret prob_space "P {i}" using prob_space by simp
+    interpret prob_space "P {i}" using proj_prob_space by simp
have R: "(space (lim\<^isub>B I P)) = (emb I {i} (Pi\<^isub>E {i} (\<lambda>_. space borel)))"
by (auto simp: prod_emb_def space_PiM)
moreover have "extensional {i} = space (P {i})" by (simp add: proj_space space_PiM)
@@ -660,7 +660,7 @@
assumes X: "J \<subseteq> I" "finite J" "\<forall>i\<in>J. B i \<in> sets borel"
shows "emeasure (lim\<^isub>B I P) (emb I J (Pi\<^isub>E J B)) = emeasure (P J) (Pi\<^isub>E J B)"
proof cases
-  interpret prob_space "P {}" using prob_space by simp
+  interpret prob_space "P {}" using proj_prob_space by simp
assume "J = {}"
moreover have "emb I {} {\<lambda>x. undefined} = space (lim\<^isub>B I P)"
by (auto simp: space_PiM prod_emb_def)
@@ -677,7 +677,7 @@
assumes "J \<subseteq> I" "finite J" "\<forall>i\<in>J. B i \<in> sets borel"
shows "measure (lim\<^isub>B I P) (emb I J (Pi\<^isub>E J B)) = measure (P J) (Pi\<^isub>E J B)"
proof -
-  interpret prob_space "P J" using prob_space assms by simp
+  interpret prob_space "P J" using proj_prob_space assms by simp
show ?thesis
using emeasure_limB_emb[OF assms]
unfolding emeasure_eq_measure limP_finite[OF `finite J` `J \<subseteq> I`] P.emeasure_eq_measure```