In some tightness condition, the existence and uniqueness of a vector measure with values in the strong dual of a quasi-barreled space is proved.

In this paper, we introduce a definition of fuzzy barreled space. On the basis, we consider a series of important theorems for fuzzy barreled space.

The definition of Fuzzy barreled space is firstly given, then the equivalent condition of Fuzzy equicontinuity on Fuzzy barreled space is discussed.