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Fuzzy set-valued stochastic Lebesgue integral

机译：模糊集值随机Lebesgue积分

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摘要

This paper studies Lebesgue integral of a fuzzy closed set-valued stochastic process with respect to the time t. Firstly, a progressively measurable fuzzy closed set-valued stochastic process is discussed and an almost everywhere problem in the former Aumann type Lebesgue integral of the level-set process is pointed out. Secondly, a new definition of the Lebesgue integral by decomposable closure is given, focusing on Aumann representation theorem, representation theorem and property of convexity. It is proved that the fuzzy closed set-valued stochastic Lebesgue integral is a fuzzy closed set-valued stochastic process which is widely used in the fuzzy world with randomness. Finally, the fuzzy closed set-valued stochastic Lebesgue integral in L~p'-space is studied, especially on an almost everywhere problem.
机译：本文研究了时间为t的模糊闭集值随机过程的Lebesgue积分。首先，讨论了一种渐进可测的模糊闭集定值随机过程，指出了水平集过程的原Aumann型Lebesgue积分中几乎到处存在的问题。其次，给出了可分解封闭的Lebesgue积分的新定义，重点是Aumann表示定理，表示定理和凸性。证明了模糊封闭集值随机Lebesgue积分是一种随机存在于模糊世界中的模糊封闭集值随机过程。最后，研究了L〜p'空间中的模糊封闭集值随机Lebesgue积分，尤其是在几乎所有问题上。

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