--- 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]