I was reading this paper by Bedford-Taylor. It was proven in Theorem 2.4 that the Monge Ampere measure $(dd^c u)^n$ has a finite mass on any polydisc when $u$ is PSH and continuous up to the boundary of the Polydisc. My question is, if $\Omega$ be a $C^1$ smooth bounded domain and $u\in PSH(\Omega)\cap C(\bar{\Omega})$ does $(dd^c u)^n$ has a finite mass on $\Omega$?
2026-03-26 17:31:27.1774546287
Complex Monge Ampere measure with finite mass
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