$\bf命题：（Riemann-Lebesgue引理）$设函数$f\left( x \right)$在$\left[ {a,b} \right]$上可积，则
\mathop {\lim }\limits_{\lambda \to {\rm{ + }}\infty } \int_a^b {f\left( x \right)\sin \lambda xdx} = 0
$\bf命题：（Riemann-Lebesgue引理的推广）$ 设函数$f\left( x \right),g\left( x \right)$均在$\left[ {a,b} \right]$上可积，且$g\left( x \right)$以正数$T$为周期，则\mathop {\lim }\limits_{\lambda \to {\rm{ + }}\infty } \int_a^b {f\left( x \right)g\left( {\lambda x} \right)dx} = \frac{1}{T}\int_0^T {g\left( x \right)dx} \int_a^b {f\left( x \right)dx}
参考答案
$\bf命题：$
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原文：http://www.cnblogs.com/ly142857/p/3715320.html