ON THE G-INTEGRABLE FUNCTION SPACE

Wang Xin;Chen Lianchang;Cheng Lixin Daqing Petroleum Institute Jianghan Petroleum Institute  

Let(s,Σ,μ) be a finite measure space, the symbol G - L(s, X~*, μ) wills tand for all (equivalence classes of)_μ - Gelfand integrable functions x~*(t):s→X~* such that||x~*(t)||= sup ∫_s|x[x~*(t)]|dμ∞ ||x||= 1Normed by the functional ||, || defined above G - L(s,X~*,μ) becomes a Banachspace.

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