which maps [sic] set to the set of all of its subsets

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James Ray 2017-11-17 17:59:09 +11:00 committed by GitHub
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@ -142,7 +142,7 @@ The definitions of the estimator and of validity appear later. For now, we denot
\end{equation*}
\end{defn}
$\mathcal{M}_0$ is the ``base case'', the set of messages with ``null justifications''. $\mathcal{M}_n$ is the set of messages at ``height'' $n$, which have messages of height $n-1$ (and/or lower) in their justification. Note that messages $\mathcal{M}_0$ have height $0$. $\mathcal{P}$ denotes the ``power set'' function, which maps set to the set of all of its subsets, so $\mathcal{P}(\bigcup_{i=0}^{n-1} \mathcal{M}_i)$ denotes all sets of protocol messages at height $n-1$ or lower.
$\mathcal{M}_0$ is the ``base case'', the set of messages with ``null justifications''. $\mathcal{M}_n$ is the set of messages at ``height'' $n$, which have messages of height $n-1$ (and/or lower) in their justification. Note that messages $\mathcal{M}_0$ have height $0$. $\mathcal{P}$ denotes the ``power set'' function, which maps a set to the set of all of its subsets, so $\mathcal{P}(\bigcup_{i=0}^{n-1} \mathcal{M}_i)$ denotes all sets of protocol messages at height $n-1$ or lower.
The estimator is a function that maps sets of protocol messages to $0$ or $1$, or a null value denoted by $\emptyset$: