An L0(F,R)-valued Function's Intermediate Value Theorem and Its Applications to Random Uniform Convexity |
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作者姓名: | Tie Xin GUO Xiao Lin ZENG |
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作者单位: | [1]LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, P. R. China [2]College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P. R. China |
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基金项目: | Supported by National Natural Science Foundation of China (Grant No. 10871016) |
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摘 要: | Let (Ω , F , P ) be a probability space and L0 ( F, R ) the algebra of equivalence classes of real- valued random variables on (Ω , F , P ). When L0 ( F, R ) is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0 ( F, R ) to L0 ( F, R ). As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module ( S,|| · ||) is random uniformly convex iff Lp ( S ) is uniformly convex for each fixed positive number p such that 1 p + ∞ .
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关 键 词: | 一致凸函数 随机变量 中值定理 应用 概率空间 概率收敛 介值定理 连续函数 |
收稿时间: | 2010-07-07 |
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