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In this paper, we consider which kind of invariant measure on hereditarysubshifts 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 a Gibbs measure where $\nu$ is an invariant measure on $(X,S)$. Asan application, we show that for some $\B$-free subshifts, the uniqueequilibrium state $\nu_\eta*B_{p,1-p}$ is not Gibbs measure.

Equilibrium states which are not Gibbs measure on hereditary subshifts