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.
Notation for infinite product measure given marginal
2
$\begingroup$
probability
measure-theory
1 Answers
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$${}{}\mu^{\otimes\mathbb N}$$
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0Hmm. That looks a little awkward. And I thought $\otimes$ was more typically used for tensor products. – 2012-09-14
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0Really? 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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0I 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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0Never 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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0OK. Thank you very much. – 2012-09-17