Let $M = (\mathbb{R}^D, \mathcal{B}(\mathbb{R}^D))$ be a D2763: Euclidean real Borel measurable space such that

(i) | $\mu, \nu : \mathcal{B}(\mathbb{R}^D) \to [0, 1]$ are each a D198: Probability measure on $M$ |

(ii) | $\mathfrak{F}_{\mu}$ and $\mathfrak{F}_{\nu}$ are each the D4131: Finite unsigned euclidean real Borel measure Fourier transform of $\mu$ and $\nu$, respectively |

Then
\begin{equation}
\mathfrak{F}_{\mu} = \mathfrak{F}_{\nu}
\quad \iff \quad
\mu = \nu
\end{equation}