
Re: Limits and Integrals
Posted:
Nov 6, 2013 11:23 AM


On Tue, 5 Nov 2013 23:02:21 0800, William Elliot <marsh@panix.com> wrote:
>If f(x,t) is uniformly continuous for x,
What does "uniformly coontinuous for x" mean?
My guess is that you mean that if we say f_x(t) = f(x,t) then the family {f_x} is (uniformly) equicontinuous. Look up the definition of "equicontinuous" and let us know...
>does > >lim(x>a) integral(r,s) f(x,t) dt > = integral(r,s) lim(x>a) f(x,t) dt ?
Yes, if my guess above is correct and lim(x>a) f(x,t) exists.
l

