Measurability on the Ordered Topological Vector Lattice

Abstract

순서 위상 벡터 격자위에서 정의된 가합의 기본성질은 H. Anton과 W.J. Pervin에 의하여 연구되었다. 이 논문에서는 그들의 방법을 확장하여 양범함수에 관한 Fatou 보조정리와 Lebesgue수렴정리에 유사한 몇개의 기본정리를 보이고, 마지막으로 순서위상벡터 격자위에서 정의된 가측의 성질을 소개하고자 한다.

The basic properties of the I-summable class S(I) on an ordered topological vector lattice has been studied by H. Anton and W.J. Pervin. Extending their methods in this paper, we are going to give some fundamental theorems which are the analogues for the positive functional I of Fatou's lemma and Lebesgue convergence theorem.

Finally, we introduce I-measurable on the ordered topological vector lattice.

The basic properties of the I-summable class S(I) on an ordered topological vector lattice has been studied by H. Anton and W.J. Pervin. Extending their methods in this paper, we are going to give some fundamental theorems which are the analogues for the positive functional I of Fatou's lemma and Lebesgue convergence theorem.

Finally, we introduce I-measurable on the ordered topological vector lattice.