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We study the convergence of volume forms on a degenerating holomorphic familyof log-Calabi-Yau varieties to a non-Archimedean measure, extending a result ofBoucksom and Jonsson. More precisely, let $(X,B)$ be a holomorphic family ofsub log canonical, log-Calabi-Yau complex varieties parameterized by thepunctured unit disk. Let $\eta$ be a meromorphic volume form on $X$ with polesalong $B$. We show that the (possibly infinite) measures induced by therestriction of the $\eta$ to a fiber converge to a measure on the Berkovichanalytification as we approach the puncture. The convergence takes place on ahybrid space, which is obtained by filling in the space $X \setminus B$ withthe aforementioned Berkovich space over the puncture.

Convergence of volume forms on a family of log-Calabi-Yau varieties to a non-Archimedean measure