- #1
takeuchi
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Let α>0, J:=[-a,a] and f:J→ℝ a bounded function.
Let α an increases monotonically on J and P* the set of all partitions P of J containing 0 and such that are symmetric,i.e, x in P iff -x in P. Prove that
∫fdα= sup L(P,f,α) with P in P*
Let α an increases monotonically on J and P* the set of all partitions P of J containing 0 and such that are symmetric,i.e, x in P iff -x in P. Prove that
∫fdα= sup L(P,f,α) with P in P*