Given a complex measure , there exists a positive measure denoted which measures the total variation of , also sometimes called simply "total variation." In particular, on a subset is the largest sum of "variations" for any subdivision of . Roughly speaking, a total variation measure is an infinitesimal version of the absolute value.
More precisely,
(1)

where the supremum is taken over all partitions of into measurable subsets .
Note that may not be the same as . When already is a positive measure, then . More generally, if is absolutely continuous, that is
(2)

then so is , and the total variation measure can be written as
(3)

The total variation measure can be used to rewrite the original measure, in analogy to the norm of a complex number. The measure has a polar representation
(4)

with .