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Let $(X,M,\mu)$ be a finite measure space and let $f$ be a real-valued and measurable function on $X$. How do I evaluate $$ \lim_{n\rightarrow \infty} \int_X ~{\left\{\cos\left(\pi f(x)\right) \right\}}^{2n}~\text{d}\mu(x)$$ in terms of $f$?

Thanks for helping.

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    You want the value of the integral or the limit as $n\to\infty$?2011-11-29
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    @JuliánAguirre yes I do. Sorry. I'll edit right away.2011-11-29

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