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Abstract We prove a general result concerning the critical probabilities of subsets of a lattice L. It is a consequence of this result that the critical probability of a percolation process on L equals the limit of the critical probability of a slice of L as the thickness of the slice tends to infinity. This verification of one of the standard hypotheses of the subject settles many questions concerning supercritical percolation.
Grimmett et al. (Wed,) studied this question.
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