Hello, Here is my original question: let $\mu$ be a singular measure with respect to the Lebesgue's measure on $R$. Is it true that $\int \psi \mu(d x)=0$ for any test function $\psi\in C_c^\infty(R)$ (smooth functions with compact support)? Following the suggestion by André Henriques, I will put the answer in the answer box. :-) Thanks again for everyone! :-) Anand p.s. this is related to [my previous post][1]. [1]: http://mathoverflow.net/questions/70146/distributions-and-measures