Behaviour of the reference measure on RCD spaces under charts

Mondino and Naber recently proved that finite dimensional RCD spaces are rectifiable. Here we show that the push-forward of the reference measure under the charts built by them is absolutely continuous with re-spect to the Lebesgue measure. This result, read in conjunction with another recent work of us, has relevant implications on the structure of tangent spaces to RCD spaces. A key tool that we use is a recent paper by De Philippis-Rindler about the structure of measures on the Euclidean space.