Stratification for the singular set of approximate harmonic maps

The aim of this note is to extend the results in Naber and Valtorta (Ann Math (2) 185:131–227, https://doi.org/10.4007/annals.2017.185.1.3, 2017) to the case of approximate harmonic maps. More precisely, we will proved that the singular strata \(\mathcal {S}^k(u)\) of an approximate harmonic map are k-rectifiable, and we will show effect bounds on the quantitative strata. In the process we will simplify many of the arguments from Naber and Valtorta (2017), and in particular we produce a new main covering lemmas which vastly simplifies the older argument.