关于凸过程的有界性和可测性

ON BOUNDEDNESS AND MEASURABILITY FOR CONVEX PROCESSES

设Ｘ是实序列完备的局部凸拓扑向量空间，Ｙ是拓扑向量空间．设Ｔ：Ｘ→２Ｙ是凸过程（ＣｏｎｖｅｘＰｒｏｃｅｓｓ），且它的定义域Ｄｏｍ（Ｔ）是Ｘ的闭子空间．本文证明了若对Ｘ上的每一可分子空间Ｍ，Ｔ在Ｍ上的限制是绝对可测的，则Ｔ是有界的．

Let X be a real sequentially complete locally convex spaceLetT:X→2Y be a convex processSuppose that the domain Dom(T) of T is a closed subspace of X In this paper we show that for every separable subspace M of X ,if the restriction T|Dom(T)∩Mis absolutely measurable,then T is bounded