A new approach to the problems of estimating the global maximum point and the integral of a continuous function on a compact set is proposed. The approach combines a simple Monte Carlo method and the ideas of the Lebesgue theory of measure and integration. Quality estimates for the proposed methods are given.

中文翻译：

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估计紧集上连续函数的全局最大值点和积分的方法

提出了一种解决紧集上连续函数的全局最大值点估计和积分问题的新方法。该方法结合了简单的 Monte Carlo 方法和 Lebesgue 测度和积分理论的思想。给出了所提出方法的质量估计。