Recent content by takeuchi

Let f:[-1,1]→ℝ an integrable function such that |f(x)|\leq2. Show that there exist x in [-1,1] such that: integral -1 to x f(t)dt-4x=0 is unique?

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*