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!

Uniform Convergence etc.

  1. Mar 15, 2006 #1
    "Suppose f_n are defined and continuous on an interval I. Assume that f_n converges uniformly to f on I. If a_n in I is a sequence and a_n -> a, prove that f_n(a_n) converges to f(a)."

    I don't understand the question. Doesn't uniform convergence imply that for all x in I and e>0, | f_n(x) - f(x) | < e? So in particular, |f_n(a_n) - f(a) | < e.
     
  2. jcsd
  3. Mar 15, 2006 #2
    Wait, nevermind. | f_n(a_n) - f(a_n) | <e, not f(a).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Uniform Convergence etc.
  1. Uniform convergence (Replies: 4)

  2. Uniform convergence (Replies: 3)

  3. Uniform convergence (Replies: 4)

Loading...