diff -r c6e9c7d140ff -r 2d79288b042c src/HOL/Analysis/Set_Integral.thy --- a/src/HOL/Analysis/Set_Integral.thy Wed Jun 21 22:57:40 2017 +0200 +++ b/src/HOL/Analysis/Set_Integral.thy Thu Jun 22 16:31:29 2017 +0100 @@ -1840,22 +1840,10 @@ translations "CLINT x:A|M. f" == "CONST complex_set_lebesgue_integral M A (\x. f)" -lemma set_borel_measurable_continuous: - fixes f :: "_ \ _::real_normed_vector" - assumes "S \ sets borel" "continuous_on S f" - shows "set_borel_measurable borel S f" -proof - - have "(\x. if x \ S then f x else 0) \ borel_measurable borel" - by (intro assms borel_measurable_continuous_on_if continuous_on_const) - also have "(\x. if x \ S then f x else 0) = (\x. indicator S x *\<^sub>R f x)" - by auto - finally show ?thesis . -qed - lemma set_measurable_continuous_on_ivl: assumes "continuous_on {a..b} (f :: real \ real)" shows "set_borel_measurable borel {a..b} f" - by (rule set_borel_measurable_continuous[OF _ assms]) simp + by (rule borel_measurable_continuous_on_indicator[OF _ assms]) simp text\This notation is from Sébastien Gouëzel: His use is not directly in line with the