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I'm wondering what the preferred notation is for denoting a (countably) infinite product measure for which all marginals are equal to some given probability measure $\mu$. Is it common, for example, to write $\mu^{\infty}$? Are there any other reasonably concise ways that this is done? Thanks in advance.

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$${}{}\mu^{\otimes\mathbb N}$$

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    Hmm. That looks a little awkward. And I thought $\otimes$ was more typically used for tensor products.2012-09-14
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    Really? How do you denote the product measure of $\mu$ and $\nu$ (the unique measure $\pi$ such that $\pi(A\times B)=\mu(A)\nu(B)$ for every suitable $A$ and $B$)?2012-09-15
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    I just use $\mu \times \nu$. Maybe $\mu^{\times N\!\!\!N}$ is OK? By the way, how to type black board bold here?2012-09-16
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    Never ever saw $\mu^{\times\mathbf N}$. // You might want to stick to blackboard `\mathbb` since fancy alternatives such as `\mathbbm` or `\mathbbold` might not render properly on this site.2012-09-16
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    OK. Thank you very much.2012-09-17