In this paper, we prove first-order asymptotics on a bounded open set of the heat content when the ambient space is an RCD(K, N) space, under a regularity condition for the boundary that we call measured interior geodesic condition of size epsilon. We carefully study such a condition, relating it to the properties of the disintegration of the signed distance function from partial differential ohm studied in Cavalletti and (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
