随机变量本性上(下)确界与范数的关系

Connection Between Essential Supremum(Infimum) and Norms for a Random Variable

给出了随机变量本性上(下)确界的2种新定义,并根据一般确界定义和概率的性质对2种新定义的等价性进行了证明;进而研究了随机变量本性上(下)确界与随机变量p范数,无穷范数之间的关系和相互表示问题.

Two new definitions of the essential supremum （infimum） of a random variable are introduced. And their equivalence is proved by use of supremum （infimum） and the properties of probability. Then the connection and representation among the essential supremum （infimum） , p-norm and infinite norm of a random variable are studied.