【摘要】 讨论了赋p-Amemiya范数‖·‖Φ,p(1<p<")的Orlicz函数空间LΦ中依测度收敛的H性质和Δ2-条件之间的关系.证明了如果Orlicz函数Φ只在零点为零,则赋p-Amemiya范数的Orlicz函数空间LΦ,p具有Hμ性质的充要条件为Φ对所有的实数满足Δ2-条件并且Φ是有限值的;如果Orlicz函数Φ不只在零点为零,则LΦ,p具有Hμ性质的充要条件为Φ在无穷远处满足Δ2-条件并且Φ是有限值的.对于Orlicz函数空间LΦ,p的由序连续的元素所构成的子空间EΦ,p,我们也证明了类似的结论.更多还原

【Abstract】 In this paper,we discuss the relationship between the property H for convergence in measure and the Δ2-condition for Orlicz function spaces LΦequipped with the p-Amemiya norm ‖·‖Φ,p( 1 < p < "). From our results it follows that if Orlicz Function Φ vanishes only at zero,then the Orlicz function spaces equipped with the p-Amemiya norm LΦ,phave property Hμif and only if Orlicz function Φ satisfies the Δ2-condition for all real numbers and Φ is finitely valued; if Φ vanishes outside zero,then LΦ,phave property Hμif and only if Φ satisfies the Δ2-condition at infinity and Φ is finitely valued. Analogous results are also proved for the subspace EΦ,pof order continuous elements of the Orlicz function space LΦ,p.更多还原