Inserted: 13 mar 2019
Last Updated: 13 mar 2019
In the existing language for tensor calculus on $\sf RCD$ spaces, tensor fields are only defined $\mathfrak m$-a.e.. In this paper we introduce the concept of tensor field defined `2-capacity-a.e.' and discuss in which sense Sobolev vector fields have a 2-capacity-a.e. uniquely defined quasi-continuous representative.