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What is the definition of a minorant?

For context, a statistics paper I am reading describes a finite sequence of positive, strictly decreasing, strictly convex sequence $\{\Gamma_n \} = \Gamma_1, \Gamma_2, \ldots \Gamma_n$. Then an estimator of this sequence (still positive but no longer strictly decreasing or convex) is $\{\hat{\Gamma}_n \} = \hat{\Gamma}_1, \hat{\Gamma}_2, \ldots \hat{\Gamma}_n$. Then what is the minorant of $k \mapsto \hat{\Gamma}_k$?

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