We consider which kind of invariant measure on hereditary subshifts is not Gibbs measure. For the hereditary closure of a subshift (X, S), we prove that in some situation, the invariant measure /nu ∗ B_{p,1-p} can not be Gibbs measure where /nu is any invariant measure on (X, S). As an application, we show that for some /mathcal{B}-free shifts, the equilibrium state /nu_/eta ∗ B_{p,1-p} is not Gibbs measure.

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