Riemann Lebesgue Lemma states that Fourier transform of an $L^1$ function, $\hat{f}(\lambda)$ is continuous and goes to zero as $|\lambda|\to \infty$. If $\mu$ is a finite nonatomic measure then is it true that $\hat{\mu}(\lambda)\to 0$? If not then is it true for some restricted class of finite measures? What are the restrictions?



Riemann-Lebesgue lemma for measures
The following web site has a review article on work related to this question:
<http://mypage.iu.edu/~rdlyons/pdf/seventy.pdf>


