Let (X, d(X), mu) be a metric measure space where X is locally compact and separable and mu is a Borel regular measure such that 0 amp;lt; mu(B(x, r)) amp;lt; infinity for every ball B(x, r) with center x is an element of X and radius r amp;gt; 0. We define chi to be the set of all positive, finite non- zero regular Borel measures with compact support in X which are dominated by mu, and M = X boolean OR {0}. By introducing a kind of mass transport metric d(M) on this set we provide a new approach to first order Sobolev spaces on metric measure spaces, first by introducing such for functions F : X -amp;gt; R, and then for functions f : X -amp;gt; [-infinity, infinity] by identifying them with the unique element F-f : X -amp;gt; R defined by the mean- value integral: Ff(eta) - 1/vertical bar vertical bar eta vertical bar vertical bar integral f d eta. In the final section we prove that the approach gives us the classical Sobolev spaces when we are working in open subsets of Euclidean space R-n with Lebesgue measure. (C) 2016 Elsevier Ltd. All rights reserved.