  In this paper we will focus on understanding the relation between Sobolev
embedding theorems for Haj{\l}asz-Besov spaces defined on a doubling metric
measure space $(\Omega,d,\mu)$ and the non-collapsing condition of the measure,
i.e. \[ \inf_{x\in\Omega}\mu(B(x,1))>0. \] We will also obtain embedding
results for Haj{\l}asz-Besov spaces whose modulus of smoothness is generated by
a rearrangement invariant quasi-norm.
