= Full-support probability distribution on a finite alphabet
{title2=$\operatorname{supp}(p)=\mathcal X$}
= Full-support finite distribution
{synonym}
A <probability mass function> $p$ has full <support of a probability distribution>[support] on a specified <finite alphabet> if $p_x>0$ for every symbol in that <alphabet>. This is relative to the chosen <alphabet>: deleting zero-probability symbols produces a smaller <alphabet> on which the same law has full <support of a probability distribution>[support]. In a weighted <prefix code> problem, full <support of a probability distribution>[support] makes every shortening of a retained <codeword> strictly reduce <expected codeword length>. Without it, a minimum-cost <code tree> may contain redundant zero-weight branches.
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