论文标题
Barndorff-Nielsen和Balakrishnan-Stepanov的定理概括到Riesz Space
Generalization of the theorems of Barndorff-Nielsen and Balakrishnan-Stepanov to Riesz spaces
论文作者
论文摘要
在Dedekind完整的Riesz Space，$ e $中，我们表明，如果$（p_n）$是$ e $ the $ e $ then $ e $ then $ e \ limsup \ limits_ {n \ to \ infty} p_n- \ liminf \ liminf \ limits_ fimits_ N \ to \ infty fy \ infty} p_n = n flims_ p_n（i-p_ {n+1}）。$$此身份用于在Dedekind完整的Riesz空间中获得有条件的扩展，该空间较弱，并且Barndorff-nielsen和Balakrishnan-Stepanov的有条件期望操作员是第一个Borel-Cantelli Theorem的概括。
In a Dedekind complete Riesz space, $E$, we show that if $(P_n)$ is a sequence of band projections in $E$ then $$\limsup\limits_{n\to \infty} P_n - \liminf\limits_{n\to \infty} P_n = \limsup\limits_{n\to \infty} P_n(I-P_{n+1}).$$ This identity is used to obtain conditional extensions in a Dedekind complete Riesz spaces with weak order unit and conditional expectation operator of the Barndorff-Nielsen and Balakrishnan-Stepanov generalizations of the First Borel-Cantelli Theorem.
