1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Riemman Stieltjes

  1. Nov 3, 2008 #1
    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*
     
  2. jcsd
  3. Nov 3, 2008 #2
    It is sufficient to show that for a given e>0, there exist a P* such that fdα-L(P*,f,α)<e.
    Find a P first and let P* be a refinement of P, which is also symmetric and containing 0. Then P* is what you want.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Riemman Stieltjes
  1. Stieltjes integral (Replies: 1)

  2. Riemman Sum Homework (Replies: 3)

  3. Riemman Sum Homework (Replies: 2)

  4. Limits & Riemman Sum (Replies: 3)

Loading...