diff -r b233f48a4d3d -r fd28b7399f2b src/HOL/Probability/Borel.thy --- a/src/HOL/Probability/Borel.thy Mon Nov 09 16:06:08 2009 +0000 +++ b/src/HOL/Probability/Borel.thy Mon Nov 09 19:42:33 2009 +0100 @@ -17,8 +17,8 @@ definition mono_convergent where "mono_convergent u f s \ - (\x m n. m \ n \ x \ s \ u m x \ u n x) \ - (\x \ s. (\i. u i x) ----> f x)" + (\x m n. m \ n \ x \ s \ u m x \ u n x) \ + (\x \ s. (\i. u i x) ----> f x)" lemma in_borel_measurable: "f \ borel_measurable M \ @@ -222,7 +222,7 @@ shows "{w \ space M. f w < g w} \ sets M" proof - have "{w \ space M. f w < g w} = - (\r\\. {w \ space M. f w < r} \ {w \ space M. r < g w })" + (\r\\. {w \ space M. f w < r} \ {w \ space M. r < g w })" by (auto simp add: Rats_dense_in_real) thus ?thesis using f g by (simp add: borel_measurable_less_iff [of f] @@ -247,7 +247,7 @@ shows "{w \ space M. f w = g w} \ sets M" proof - have "{w \ space M. f w = g w} = - {w \ space M. f w \ g w} \ {w \ space M. g w \ f w}" + {w \ space M. f w \ g w} \ {w \ space M. g w \ f w}" by auto thus ?thesis using f g by (simp add: borel_measurable_leq_borel_measurable Int)