摘要
对实变函数论中的Ｌｅｖｉ定理在空间Ｌ＾ｐ「Ｊ，Ｅ」＝｛ｆ（ｘ）│ｆ（ｘ）：Ｊ→Ｅ是强可测函数，∫∥ｆ（ｘ）∥ｐｄｘ〈＋∞｝中进行了讨论，由此得到抽象函数Ｌｅｖｉ定理的几种形式；并得出Ｅ中锥正规、正则、全正则等价于Ｌ＾ｐ「Ｊ，Ｅ」中的锥有相应的性质。
Levi theorems in L￣p [J, E] = {f(x) | f: J→E is strongly measurable, and J. ‖ f(x)‖ .dx<+∞ } (where J = [a, b] =R, E is a Banach space, 1≤ ρ<+∞ )are discussed, and several forms of Levi theorem of abstract functions are get. The paper also comes to the conclusion that a cone P of E is normal(regular or fully regular)if the cone P of Lp[J,E] induced by P has the corresponding property.
出处
《山东大学学报（自然科学版）》
CSCD
1995年第4期418-424,共7页
Journal of Shandong University(Natural Science Edition)
