This paper discusses the properties of Skorokhod metric on normal and upper semi-continuous fuzzy sets space. All mentioned below refer to this type sets. We confirm that enhanced-type are equivalent compact However, not necessarily L p -integrable sets, which include point out -type d metric, ≥ 1 , is well-defined in common cases but always all introduce ⁎ an expansion write as sequel. Then, w...

We study the properties of dual Sobolev space $H^{-1, q}(\mathbb{X}) = \big(H^{1, p}(\mathbb{X})\big)'$ on a complete extended metric-topological measure $\mathbb{X} (X, \tau, \rm{d}, \rm{m})$ for $p\in (1, \infty)$. will show that crucial role is played by strong closure $H_{{\rm{pd}}}^{ - 1, q}\left({\mathbb{X}} \right)$ $L^q(X, in q}(\mathbb{X})$, which can be identified with predual $H^{1, ...

We explore the relationship in metric spaces between different properties related to Besicovitch covering theorem, and also consider weak versions of doubling, connection non-uniqueness centers radii arbitrary spaces.