Under volume doubling and weak (1,p)-Poincaré inequalities, p-massiveness of infinite connected sets on weighted graphs is equivalent to a dyadic relative p-capacity condition in nested balls.
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A Wiener criterion at infinity for $p$-massiveness on weighted graphs
Under volume doubling and weak (1,p)-Poincaré inequalities, p-massiveness of infinite connected sets on weighted graphs is equivalent to a dyadic relative p-capacity condition in nested balls.