This article presents a concise proof of the famous Benford's law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and elegant, accessible to anyone with basic knowledge of calculus, revealing that the law originates from the basic property of the human number system. The criterion can bring great convenience to the field of fraud detection.

翻译：本文针对具有黎曼可积概率密度函数的分布，给出了著名本福德定律的一个简明证明，并提供了判断分布是否遵循该定律的判据。该证明直观而优雅，只需具备微积分基础知识即可理解，揭示了该定律源于人类数字系统的基本特性。该判据可为欺诈检测领域带来极大便利。