论文标题
Monge-Ampère措施平等
An equality of Monge-Ampère measures
论文作者
论文摘要
令$ u $和$ v $是Monge-ampèreOperator在域上的定义域$ω\ subset {\ bf c}^n $的域中的两个plurisubharmonic函数。我们证明，如果$ u = v $在plurifinely Open设置$ u \ u \ subsetω$中，则可以测量，然后$（dd^cu）^n | _u =（dd^cv）^n | _u $。贝德福德（Bedford）和泰勒（Taylor）证明了$ u $和$ v $在本地界限的情况下，当$ u $和$ v $有限时，el kadiri和wiegerinck是有限的； $ψ_j$，$ j = 1，...，m $是$ω$上的plurisubharmonic函数。
Let $u$ and $v$ be two plurisubharmonic functions in the domain of definition of the Monge-Ampère operator on a domain $Ω\subset {\bf C}^n$. We prove that if $u=v$ on a plurifinely open set $U\subset Ω$ that is Borel measurable, then $(dd^cu)^n|_U=(dd^cv)^n|_U$. This result was proved by Bedford and Taylor in the case where $u$ and $v$ are locally bounded, and by El Kadiri and Wiegerinck when $u$ and $v$ are finite, and by Hai and Hiep when $U$ is of the form $U=\bigcup_{j=1}^m\{φ_j>ψ_j\}$, where $φ_j$, $ψ_j$, $j=1,...,m$, are plurisubharmonic functions on $Ω$.
