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讨论了Sugeno测度这类有代表性的非可加测度的性质,给出了Sugeno测度空间上的gλ随机变量及其分布函数、期望和方差的定义及性质,证明了Sugeno测度空间上的Markov不等式、Chebyshev不等式和Khinchine大数定律;给出了Sugeno测度空间上的经验风险泛函、期望风险泛函以及ERM原则严格一致收敛的定义,在此基础上给出并证明了Sugeno测度空间上的学习理论的关键定理、学习过程一致收敛速度的界以及这些界与函数集容量之间的关系.
We discuss the properties of Sugeno measure, such as representative non-additive measure, and give the definition and properties of gλ stochastic variables in Sugeno measure space and its distribution function, expectation and variance. We prove that the Markov inequality in Sugeno measure space , Chebyshev’s inequality and Khinchine’s Law of Large Numbers are introduced. The definitions of empirical risk functional in Sugeno measure space, expectant risk functional and strictly consistent convergence of ERM are given. Based on this, the learning of Sugeno measure space is given and proved The key theorem of theorem, the convergence speed of the learning process, and the relationship between these functions and the capacity of the function set.