= A good rate function is separated from zero away from its minimizer
If a <good rate function> has unique zero mu, every <closed set> missing mu has strictly positive <infimum> rate, possibly infinity. Otherwise a sequence of rates tending to zero lies eventually in the compact unit <sublevel set>; a subsequence converges to a point of the <closed set>, and <lower semicontinuity> makes that point another zero. Compactness also ensures existence of a zero whenever the <infimum> is zero.
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