关键词: Sugeno测度空间, 准范数, 复经验风险最小化原则, 关键定理, 收敛速度的界

Abstract: Firstly，the definitions of complex g_λ random variable and primary norm are introduced.Next the concepts and some properties of the mathematical expectation and variance of complex g_λ random variables are provided.Secondly，for complex g_λ random variables，a number of fundamental concepts such as e.g.，Markov’s inequalities，Chebyshev’s inequalities and a Khinchine’s law of large numbers are discussed.Finally，the definitions of the complex empirical risk functional，the complex expected risk functional and complex empirical risk minimization principle on Sugeno measure space are proposed.Then the key theorem of learning theory based on complex g_λ random samples is proved，and the bounds on the rate of uniform convergence of learning process are constructed.The investigations help lay essential theoretical foundations for the systematic and comprehensive development of the statistical learning theory of complex g_λ random samples.

Key words: Sugeno measure space, primary norm, complex empirical risk minimization principle, the key theorem, the bounds on the rate of convergence