An equivalent condition for a measure on $\mathbb{T}$ to be symmetric

Is it correct that a Borel probability measure $\sigma$ on the complex unit circle $\mathbb{T}$ is symmetric (i.e. $\sigma(A)=\sigma(\overline{A})$ for every Borel set) iff $\hat{\sigma}(n)=\hat{\sigma}(-n)$ for every $n\in\mathbb{Z}$?

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