集值下鞅的一类Riesz分解

A Class of Riesz Decomposition for Set-Valued Submartingle

举例说明即使在一维实空间,集值下鞅并非都可Riesz分解,即集值下鞅表示为集值鞅与集值下鞅之和.给出集值下鞅一种新的Riesz分解定义,证明了一维实空间集值下鞅有该种形式的Riesz分解,并举例说明在二维实空间,集值下鞅不具有这种形式的Riesz分解.最后证明了集值下鞅具有这种形式Riesz分解的充分必要条件.

Some certain examples were mentioned in order to prove that not all the set-valued submartingle could be decomposed even in one dimension real space. In other words, the set-valued submartingle means the sum of set-valued martingle and set-valued submartingle. A new definition about the Riesz decomposition of set-valued submartingle was presented. We proved that the set-valued submartingle possesses the new form of definition in one dimension real space. In order to illustrate that the new definition is not available in two- dimension real space, some examples were given here. At last, we gave and proved that the sufficient and necessary conditions of this new Riesz decomposition.