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It is shown that a locally integrable function f on R" has bounded lower oscillation (f E BLO) if and only if f = MF + h, where F has bounded mean oscillation (F E BMO) and MF < oo a.e., and h is bounded. Here, MF is a variant of the familiar Hardy-Littlewood maximal function: MF = SUpQ 3 X Q( F) (no absolute values), where Q( F) is the mean value of F over the cube Q.