How Is the Variation of a Complex Charge Determined with Disjunctive Charges?

[Fermat1]

Let (X,R) be a measure space. \(\displaystyle v=u_{1}+iu_{2}\) be a complex charge. Find the variation of v when \(\displaystyle u_{1}, u_{2}\) are positive disjunctive charges.

Does disjunctive charges mean that there is a partition A, B of X such that \(\displaystyle u_{1}(A)= u_{2}(B)=0\)?

 

[Jhoneine]

If this is the case, then the variation of v is defined as:Var(v) = |u_{1}| + |u_{2}| = max{u_{1}, u_{2}}.