Abstract: In this paper, the authors investigate the completeness and closure of random systems{ t^{λn (ω)} } in the weighted Banach space $C_{\alpha}$, where $C_{\alpha}$ denotes the Banach spaces consisting of functions of one complex variable continuous on the right half real axis and satisfying $|f(t)|{\rm e}^{-\alpha(t)}\rightarrow0~(t\rightarrow +\infty$).

Key words: Weighted Banach spaces, Random systems, Closure