I'm reading 'Navier-Stokes flow in $\mathbb{R}^3$ with measures as initial vorticity and Morrey spaces' (a paper of Giga and Miyakawa) but there is something that I don't untherstand about the definition of Morrey spaces they give.

They introduce them (for each $1\leq p\leq \infty$) as the spaces of Radon signed measures $\mu$ in $\mathbb{R}^N$ verifying:

$$\Vert \mu\Vert_p:=\sup\limits_{x\in \mathbb{R}^N,r>0} r^{-\frac{N}{p'}}\cdot \vert\mu\vert(B(x,r))<\infty$$

They proof that $\Vert \cdot \Vert_p$ is a Banach norm, but I don't understand how could one sum two Radon signed measure without having problems at computing $+\infty-\infty$. Notice that we are NOT asuming $\mu$ to have finite total variation.

Could anyone help me? Thanks.

PD: Sorry for my English.