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Minor Math Jaxing
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Daniele Tampieri
Daniele Tampieri
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Take a uniform distribution on the circle of radius $1 - 2^{-n)$$1 - 2^{-n}$. These have disjoint support & so total variation distance is 1, but for a given measure the projections are all the same, and they are absolutely continuous 1-d measures & quite similar.

Take a uniform distribution on the circle of radius $1 - 2^{-n)$. These have disjoint support & so total variation distance is 1, but for a given measure the projections are all the same, and they are absolutely continuous 1-d measures & quite similar.

Take a uniform distribution on the circle of radius $1 - 2^{-n}$. These have disjoint support & so total variation distance is 1, but for a given measure the projections are all the same, and they are absolutely continuous 1-d measures & quite similar.

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mike
mike
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Take a uniform distribution on the circle of radius $1 - 2^{-n)$. These have disjoint support & so total variation distance is 1, but for a given measure the projections are all the same, and they are absolutely continuous 1-d measures & quite similar.