The meaning of subscripts + and - under the difference of measures

Question

Let $\mu, \nu$ be two bounded measures on a measurable space $(\Omega, \mathcal{A})$. What does the following notation mean?

$(\mu - \nu)_{+}(\Omega) + (\mu - \nu)_{-}(\Omega)$

What does $(\mu - \nu)_{+/-}$ mean?

Answer 1

The commend by Did was an answer:

For every signed bounded measure $\rho$ and every $A$ in $\mathcal A$, $$\rho_+(A)=\sup\{\rho(B)\mid B\in\mathcal A,B\subseteq A\}.$$ Likewise, $$\rho_-=(-\rho)_+.$$ Then, for every $A$ in $\mathcal A$, $$\rho(A)=\rho_+(A)-\rho_-(A),$$ and one defines $$|\rho|=\rho_+ +\rho_-.$$

Related topic: Jordan measure decomposition