广义拟容量的C-右连续性

本文探讨广义容量的性质，得到如下结果：（a）具有C-右连续，即关于紧集连续的凸拟容量是凸容量；（b）一大类广义容量具有C-右连续性；（c）凸拟容量的准上积分是凸Choquet容量．此外，给出具有C-右连续性的弱拟容量的可容性定理．本文还利用上述结果研究调和空间上正超调和函数的缩减函数和扫除函数．

The G-Right Continuity of Generalized Pre-capacities

This paper studies the properties of some generalized capacities and proves (a) any convex pre-capacity is a convex capacity if it has the C-right continuity, i. e. , a continuity with respect to compact sets , (b) there is a large sort of generalized capacities which have the C-right continuity; (c) the pseudo-upper-integral of any convex pre-capacity is a convex Choquet capacity. And a capacitability theorem is obtained for the weak pre-capacity with the C-right continuity. These results are also used to investigate the reduced and balayaged functions of positive hyperharmonic functions on harmonic spaces.