论文标题
概括和几乎所有地方融合的新证明
Generalization and New Proof for Almost Everywhere Convergence to Imply Local Convergence in Measure
论文作者
论文摘要
通过一种新的证明方法，我们在更一般的设定经典收敛定理中证明，几乎到处可测量的函数在有限测量空间上的融合意味着衡量的收敛性。具体而言，我们将代码剂是可分开的度量空间以及限制映射恒定并且代码域是任意拓扑空间的情况下概括了定理。
With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize the theorem for the case where the codomain is a separable metric space and for the case where the limiting map is constant and the codomain is an arbitrary topological space.
