论文标题
在当地紧凑的空间上的措施
Balayage of measures on a locally compact space
论文作者
论文摘要
我们在本地紧凑型空间上$ x $ $ x $ $ a \ subset x $在$ \ mathbb r^n $，$ n \ geqslant3 $上概括了newtonian inner balayage理论，从而在本地紧凑型$ a \ subset x $上开发了一个正ra量的内部巴莱奇。为了确定该理论的应用，我们表明，如果Space $ x $完全正常，并且$k_σ$的级别，那么Bent Fuglede（Anal。Math。，2016）的最新结果对Quasiclosed $ a $ a $ a $的外部balayage对$μ$ a $仍然有效。我们特别给出了内部（外部）balayage的各种替代定义，为评估其总质量提供了一种公式，并证明了内部（外部）扫描度量及其潜力的收敛定理。在$ \ mathbb r^n $，$ n \ geqslant2 $上，获得的大多数古典内核确实保留（部分是新的），这在应用程序中很重要。
We develop a theory of inner balayage of a positive Radon measure $μ$ of finite energy on a locally compact space $X$ to arbitrary $A\subset X$, generalizing Cartan's theory of Newtonian inner balayage on $\mathbb R^n$, $n\geqslant3$, to a suitable function kernel on $X$. As an application of the theory thereby established, we show that if the space $X$ is perfectly normal and of class $K_σ$, then a recent result by Bent Fuglede (Anal. Math., 2016) on outer balayage of $μ$ to quasiclosed $A$ remains valid for arbitrary Borel $A$. We give in particular various alternative definitions of inner (outer) balayage, provide a formula for evaluation of its total mass, and prove convergence theorems for inner (outer) swept measures and their potentials. The results obtained do hold (and are new in part) for most classical kernels on $\mathbb R^n$, $n\geqslant2$, which is important in applications.
