equal
deleted
inserted
replaced
4920 lemma negligible_translation_rev: |
4920 lemma negligible_translation_rev: |
4921 assumes "negligible ((+) c ` S)" |
4921 assumes "negligible ((+) c ` S)" |
4922 shows "negligible S" |
4922 shows "negligible S" |
4923 by (metis negligible_translation [OF assms, of "-c"] translation_galois) |
4923 by (metis negligible_translation [OF assms, of "-c"] translation_galois) |
4924 |
4924 |
|
4925 lemma negligible_atLeastAtMostI: "b \<le> a \<Longrightarrow> negligible {a..(b::real)}" |
|
4926 using negligible_insert by fastforce |
|
4927 |
4925 lemma has_integral_spike_set_eq: |
4928 lemma has_integral_spike_set_eq: |
4926 fixes f :: "'n::euclidean_space \<Rightarrow> 'a::banach" |
4929 fixes f :: "'n::euclidean_space \<Rightarrow> 'a::banach" |
4927 assumes "negligible {x \<in> S - T. f x \<noteq> 0}" "negligible {x \<in> T - S. f x \<noteq> 0}" |
4930 assumes "negligible {x \<in> S - T. f x \<noteq> 0}" "negligible {x \<in> T - S. f x \<noteq> 0}" |
4928 shows "(f has_integral y) S \<longleftrightarrow> (f has_integral y) T" |
4931 shows "(f has_integral y) S \<longleftrightarrow> (f has_integral y) T" |
4929 proof - |
4932 proof - |