equal
deleted
inserted
replaced
144 "interval_lebesgue_integral M a b f = |
144 "interval_lebesgue_integral M a b f = |
145 (if a \<le> b then (LINT x:einterval a b|M. f x) else - (LINT x:einterval b a|M. f x))" |
145 (if a \<le> b then (LINT x:einterval a b|M. f x) else - (LINT x:einterval b a|M. f x))" |
146 |
146 |
147 syntax |
147 syntax |
148 "_ascii_interval_lebesgue_integral" :: "pttrn \<Rightarrow> real \<Rightarrow> real \<Rightarrow> real measure \<Rightarrow> real \<Rightarrow> real" |
148 "_ascii_interval_lebesgue_integral" :: "pttrn \<Rightarrow> real \<Rightarrow> real \<Rightarrow> real measure \<Rightarrow> real \<Rightarrow> real" |
149 ("(5LINT _=_.._|_. _)" [0,60,60,61,100] 60) |
149 (\<open>(5LINT _=_.._|_. _)\<close> [0,60,60,61,100] 60) |
150 |
150 |
151 syntax_consts |
151 syntax_consts |
152 "_ascii_interval_lebesgue_integral" == interval_lebesgue_integral |
152 "_ascii_interval_lebesgue_integral" == interval_lebesgue_integral |
153 |
153 |
154 translations |
154 translations |
158 "interval_lebesgue_integrable M a b f = |
158 "interval_lebesgue_integrable M a b f = |
159 (if a \<le> b then set_integrable M (einterval a b) f else set_integrable M (einterval b a) f)" |
159 (if a \<le> b then set_integrable M (einterval a b) f else set_integrable M (einterval b a) f)" |
160 |
160 |
161 syntax |
161 syntax |
162 "_ascii_interval_lebesgue_borel_integral" :: "pttrn \<Rightarrow> real \<Rightarrow> real \<Rightarrow> real \<Rightarrow> real" |
162 "_ascii_interval_lebesgue_borel_integral" :: "pttrn \<Rightarrow> real \<Rightarrow> real \<Rightarrow> real \<Rightarrow> real" |
163 ("(4LBINT _=_.._. _)" [0,60,60,61] 60) |
163 (\<open>(4LBINT _=_.._. _)\<close> [0,60,60,61] 60) |
164 |
164 |
165 syntax_consts |
165 syntax_consts |
166 "_ascii_interval_lebesgue_borel_integral" == interval_lebesgue_integral |
166 "_ascii_interval_lebesgue_borel_integral" == interval_lebesgue_integral |
167 |
167 |
168 translations |
168 translations |
1047 by (simp add: ac_simps) |
1047 by (simp add: ac_simps) |
1048 qed |
1048 qed |
1049 |
1049 |
1050 |
1050 |
1051 syntax "_complex_lebesgue_borel_integral" :: "pttrn \<Rightarrow> real \<Rightarrow> complex" |
1051 syntax "_complex_lebesgue_borel_integral" :: "pttrn \<Rightarrow> real \<Rightarrow> complex" |
1052 ("(2CLBINT _. _)" [0,60] 60) |
1052 (\<open>(2CLBINT _. _)\<close> [0,60] 60) |
1053 |
1053 |
1054 syntax_consts |
1054 syntax_consts |
1055 "_complex_lebesgue_borel_integral" == complex_lebesgue_integral |
1055 "_complex_lebesgue_borel_integral" == complex_lebesgue_integral |
1056 |
1056 |
1057 translations "CLBINT x. f" == "CONST complex_lebesgue_integral CONST lborel (\<lambda>x. f)" |
1057 translations "CLBINT x. f" == "CONST complex_lebesgue_integral CONST lborel (\<lambda>x. f)" |
1058 |
1058 |
1059 syntax "_complex_set_lebesgue_borel_integral" :: "pttrn \<Rightarrow> real set \<Rightarrow> real \<Rightarrow> complex" |
1059 syntax "_complex_set_lebesgue_borel_integral" :: "pttrn \<Rightarrow> real set \<Rightarrow> real \<Rightarrow> complex" |
1060 ("(3CLBINT _:_. _)" [0,60,61] 60) |
1060 (\<open>(3CLBINT _:_. _)\<close> [0,60,61] 60) |
1061 |
1061 |
1062 syntax_consts |
1062 syntax_consts |
1063 "_complex_set_lebesgue_borel_integral" == complex_set_lebesgue_integral |
1063 "_complex_set_lebesgue_borel_integral" == complex_set_lebesgue_integral |
1064 |
1064 |
1065 translations |
1065 translations |
1073 "real measure \<Rightarrow> ereal \<Rightarrow> ereal \<Rightarrow> (real \<Rightarrow> complex) \<Rightarrow> bool" where |
1073 "real measure \<Rightarrow> ereal \<Rightarrow> ereal \<Rightarrow> (real \<Rightarrow> complex) \<Rightarrow> bool" where |
1074 "complex_interval_lebesgue_integrable M a b f \<equiv> interval_lebesgue_integrable M a b f" |
1074 "complex_interval_lebesgue_integrable M a b f \<equiv> interval_lebesgue_integrable M a b f" |
1075 |
1075 |
1076 syntax |
1076 syntax |
1077 "_ascii_complex_interval_lebesgue_borel_integral" :: "pttrn \<Rightarrow> ereal \<Rightarrow> ereal \<Rightarrow> real \<Rightarrow> complex" |
1077 "_ascii_complex_interval_lebesgue_borel_integral" :: "pttrn \<Rightarrow> ereal \<Rightarrow> ereal \<Rightarrow> real \<Rightarrow> complex" |
1078 ("(4CLBINT _=_.._. _)" [0,60,60,61] 60) |
1078 (\<open>(4CLBINT _=_.._. _)\<close> [0,60,60,61] 60) |
1079 |
1079 |
1080 syntax_consts |
1080 syntax_consts |
1081 "_ascii_complex_interval_lebesgue_borel_integral" == complex_interval_lebesgue_integral |
1081 "_ascii_complex_interval_lebesgue_borel_integral" == complex_interval_lebesgue_integral |
1082 |
1082 |
1083 translations |
1083 translations |