Similarly to the decomposition $L_2(\mathbb R^n) = L_2(\mathbb{R})^{\otimes n}$ as vector spaces (and even as Hilbert spaces) , do we have $bm(\mathbb{R^n}) = bm(\mathbb{R})^{\otimes n}$

where $bm(\mathbb{R})$ refers to the space of borel measures over the reals?

The reason I was thinking of this decomposition is because we have such a decomposition for the $\sigma$-algebras $\mathbf{B}(\mathbb{R^n})$ and the construction of product measures as product of marginales measures is similar to the wa the isomorphism between the $l_2$ spaces is constructed.

Thank you