Prove Lim N→∞ of Rudin Fourier Series 8.19

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Rudin 8.19
f is a continuous function on R, f(x+2Pi)=f(x), and a/pi is irrational.
Prove that

lim N goes to infinity (Sum n=1,...,N f(x+na)) =(1/2pi) * \int f(t)dt from -pi to pi
for every x.

Hint: do it first for f(x)=exp(ikx)

THANKS!
 
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welcome to pf!

hi 220205! welcome to pf! :wink:

hint: do it first for f(x)=exp(ikx) :smile:
 


tiny-tim said:
hi 220205! welcome to pf! :wink:

hint: do it first for f(x)=exp(ikx) :smile:

Thanks!
 
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