src/HOL/Analysis/Lebesgue_Integral_Substitution.thy
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     4     Provides lemmas for integration by substitution for the basic integral types.
     4     Provides lemmas for integration by substitution for the basic integral types.
     5     Note that the substitution function must have a nonnegative derivative.
     5     Note that the substitution function must have a nonnegative derivative.
     6     This could probably be weakened somehow.
     6     This could probably be weakened somehow.
     7 *)
     7 *)
     8 
     8 
     9 section \<open>Integration by Substition for the Lebesgue integral\<close>
     9 section \<open>Integration by Substition for the Lebesgue Integral\<close>
    10 
    10 
    11 theory Lebesgue_Integral_Substitution
    11 theory Lebesgue_Integral_Substitution
    12 imports Interval_Integral
    12 imports Interval_Integral
    13 begin
    13 begin
    14 
    14