The nonexistence of “liftings” for arithmetic density
The nonexistence of “liftings” for arithmetic density
P. Erdös, answering a question of D. Maharam, proved that arithmetic density as a set function does not admit an analogue of measure theoretic liftings [<bold>1</bold>, Theorem <bold>4</bold>]. Here we give a quick proof of this which works in a slightly more general situation.