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Topic: Limits and Integrals
Replies: 3   Last Post: Nov 7, 2013 12:08 PM

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David C. Ullrich

Posts: 3,112
Registered: 12/13/04
Re: Limits and Integrals
Posted: Nov 6, 2013 11:23 AM
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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





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