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Christian Remling
Christian Remling
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Does Is the space of all borel measures on R^n is$\mathbb R^n$ isomorphic to the tensor product of spaces of borel measures on R$\mathbb R$?

Similarly to the decomposition $l_2(\mathbb{R^n}) = l_2(\mathbb{R})^{\otimes n}$$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

Does the space of all borel measures on R^n is isomorphic to the tensor product of spaces of borel measures on R?

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

Is the space of all borel measures on $\mathbb R^n$ isomorphic to the tensor product of spaces of borel measures on $\mathbb R$?

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

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Elesthor
Elesthor
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Does the space of all borel measures on R^n is isomorphic to the tensor product of spaces of borel measures on R?

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