A similar question on this site addresses the general word for the measurement itself, e.g. count in zero dimensions, length in one, area in two, volume in three, and $n$-volume/area or - more generally - measure for higher dimensions.
Is there a corresponding term in the mathematical lexicon for the differential element? I haven't seen anything like it in glossaries like Mathworld which seems to only go as high as three dimensions.
Would something like "measure element" be appropriate?