src/HOL/Probability/Bochner_Integration.thy
changeset 61945 1135b8de26c3
parent 61942 f02b26f7d39d
child 61969 e01015e49041
--- a/src/HOL/Probability/Bochner_Integration.thy	Mon Dec 28 01:26:34 2015 +0100
+++ b/src/HOL/Probability/Bochner_Integration.thy	Mon Dec 28 01:28:28 2015 +0100
@@ -2352,7 +2352,7 @@
 
 lemma integral_0_iff:
   fixes f :: "'a \<Rightarrow> real"
-  shows "integrable M f \<Longrightarrow> (\<integral>x. abs (f x) \<partial>M) = 0 \<longleftrightarrow> emeasure M {x\<in>space M. f x \<noteq> 0} = 0"
+  shows "integrable M f \<Longrightarrow> (\<integral>x. \<bar>f x\<bar> \<partial>M) = 0 \<longleftrightarrow> emeasure M {x\<in>space M. f x \<noteq> 0} = 0"
   using integral_norm_eq_0_iff[of M f] by simp
 
 lemma (in finite_measure) integrable_const[intro!, simp]: "integrable M (\<lambda>x. a)"