On 12/12/06, Daniel Lakeland <dlakelan at street-artists.org> wrote:
> Ok, thanks to a different off-list example from stavros I see that for
> my intuitive idea to hold requires at least that the periodic function
> have non-zero integral over one period. otherwise a periodic function
> like one that is 1 at every integer and 0 everywhere else will
> obviously hammer the integral to zero.
My counterexample had non-zero integral over each period. The example was:
f(x) := if evenp(floor(x)) then 1 else 0$
p(x) := if evenp(floor(x)) then 0 else 1$
p is a periodic function with period = 2 and integral over the period = 1.
integral(f(x),x,0,inf) clearly diverges
integral(p(x)*f(x),x,0,inf) = 0.
-s