Pettis可积性、向量测度的表示和具Schur性质的L'X(μ)特征

PETTIS INTEGRAL,REPRESENTATION OF VECTOR MEASURE AND L ′ X(μ)

讨论了Ｐｅｔｉｓ可积向量值函数ｆ与线性算子Ｔ：ｘ＊→Ｌ１（μ）的关系；在域上Ｐｅｔｉｓ可积在一定条件下也在其σ－域上Ｐｅｔｉｓ可积；给出了可数可加向量测度Ｇ：∑→Ｘ＊的ｗ＊可测函数的一个表示定理．

The author discussed the relation between Pettis integral vector function f and linear operation T:X →L 1(μ) and relation between Banach space X with schur property and weak convergence in L ′ X(μ) , gave a representation theorem for w  measurable function of countable additive vector measure G:Σ→X  ,and a result that pettis integral function in domain is also Pettis integrable in σ domain.