Properties of first-order Sobolev-type spaces on abstract metric measure
spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are
investigated. The set of all weak upper gradients of a Newtonian function is of
particular interest. Existence of minimal weak upper gradients in this general
setting is proven and corresponding representation formulae are given.
Furthermore, the connection between pointwise convergence of a sequence of
Newtonian functions and its convergence in norm is studied
