Choquet积分与上泛积分等价的一个充分条件

A Sufficient Condition for the Equivalence of the Choquet Integral and the Pan-integral from Above

首先证明了Choquet积分不大于上泛积分的充分必要条件是单调测度μ具有次可加性;其次在μ满足一个新结构特性的假设下,通过构造简单函数,证明了Choquet积分不小于上泛积分,从而给出了Choquet积分与上泛积分一致的一个充分条件.

Firstly,it proves that the Choquet integral is less than or equal to the pan integral from above if and only if the monotone measure is subadditive.Then,by constructing a sequence of simple functions,it proves that the Choquet integral is larger than or equal to the pan-integral from above whenever the monotone measure satisfies a new structural characteristic.Thus,it provides a sufficient condition such that the Choquet integral coincides with the pan-integral from above.