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This is standard notation in information theory but it is redundant as given here, usually it is used as below. For example $P_M(m)$ would be used instead of $P_M(M=m)$ both of which refer to the random variable $M$ and the probability that it equals $m$. $P_{M,X}(M=m,X=x)=P_{M,X}(m,x)$ would refer to a joint distribution in the same way.

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