LAUSR

We present ten different characterizations of functions satisfying a weak reverse Hölder inequality on an open subset of a metric measure space with a doubling measure. Among others, we describe these functions as a class of weak $$A_\infty $$ A ∞ weights, which is a generalization of Muckenhoupt weights that allows for nondoubling weights. Although our main results are modeled after conditions that hold true for Muckenhoupt weights, we also discuss two conditions for Muckenhoupt $$A_\infty $$ A ∞ weights that fail to hold for weak $$A_\infty $$ A ∞ weights.