Levy theorem states that if $(\mu_n)_n$ is a sequence of probability measures on $\mathbb{R}^d$ such that the sequence of Fourier transforms $(\mathcal{F}(\mu_n))_n$ converges pointwise to a function $f\colon\mathbb{R}^d\to\mathbb{R}$ that is continuous at $0$, then there exists a unique probability $\mu$ with $\mathcal{F}(\mu)=f$, and $(\mu_n)$ tends weakly to $\mu$ in $\mathbb{R}^d$.

The question: Is there a version for signed bounded measures on $\mathbb{R}^d$.

Thanks in advance.

yor Levi with ani? $\endgroup$ – Mariano Suárez-Álvarez May 8 '11 at 22:25eand with a finaly. $\endgroup$ – Michael Hardy May 9 '11 at 1:42