Summary: Let \(\mu\) be a positive Radon measure in \(\mathbb R^n\) with compact support \(\Gamma\). Let \(Q_{jm}\) be cubes with side-length \(2^{-j+1}\) originating from the canonical tiling of \(\mathbb R^n\) where \(j\in \mathbb N_0\) and \(m\in \mathbb Z^n\). If \(\lambda \in \mathbb R\), \(0<p\leq\infty\), \(0<q\leq\infty \), then \(\mu^\lambda_{pq}\) is the mixed \(\ell_q\)-\(\ell_p\)-quasi-norm of the sequence \(2^{j\lambda}\mu(Q_{jm})\). Quantities of this type are considered in fractal geometry (multifractal formalism) and in the theory of the function spaces \(B^s_{pq}(\mathbb R^n)\) and \(F^s_{pq}(\mathbb R^n)\). In Theorem 1 we deal with the question when \(\mu^\lambda_{pq}\) is an equivalent quasi-norm in some of these spaces (\(\mu\)-property). If \(|\Gamma| = 0\), then \(S_\mu\) consists of those points \((t,s)\) in the \(t\)-\(s\)-diagram in Figure 1 for which \(\mu\) belongs to \(B^s_{p\infty}(\mathbb R^n)\) with \(pt=1\). Theorem 2 deals with the interrelation of \(S_\mu\) and \(\mu^\lambda_{pq}\). Some applications to truncated Riesz potentials, Bessel potentials and Fourier transforms of \(\mu\) are given.