A completely additive set function von a measurable space (2) which assumes at most one of the values + and - and satisfies v!)-0 is sometimes called a signed measure. If v is a signed measure on a measurable space (F) and "[4] = sup(B): 48e, then y" is a measure satisfying v(4) 2 (A). AF Likewise, [4)--inf((B): ABF) is a measure with [4]-[4]: the measures and are called the upper and lower variations respectively and the representation --vis the Jordan decomposition of v. If vise-finite, so are and 6 If As F. is the Jordan decomposition (Exercise 5) of the signed measure, then is a measure called the total variation of v. Clearly, 44].