S-闭空间的测度(Ⅱ)(英文)

THE MEASURE ON S CLOSED SPACES(Ⅱ)

继续讨论了Ｓ－闭空间的测度．首先得到了：当Ｘ是Ｓ－闭空间，则Ｃ（Ｘ）上的对偶空间与Ｘ上有界Ｆ－Ｓ测度一致；

If X is a compact space, many important results can be obtained in the C(X). In , a measure on S closed spaces was constructed. Some S closed spaces are neither compact nor Hausdorff, but some interesting results can still be obtained. In this paper, we continuously discuss the properties of the measure on S closed spaces, and then get some of the very interesting conclusions. For example, if X is an S closed space, the dual of C(X) is the space of all finite signed F S measure on X with norm defined by ‖v‖=|v|(X). In addition we obtain∫fdu=0if and only if f≡0 on U for each nonnegative F S measurable continuous function f and F S measure u.