src/HOL/Analysis/Interval_Integral.thy
changeset 80914 d97fdabd9e2b
parent 80768 c7723cc15de8
child 81097 6c81cdca5b82
equal deleted inserted replaced
80913:46f59511b7bb 80914:d97fdabd9e2b
   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