Lebesgue积分题若f是[a,b]上Lebesgue可积函数,证明:当n→∞时,∫(a→b)f(x)|sinnx|dx=2/π*∫(a→b)f(x)dx有能做出来的或者能提供思路的都行啊……好的必有重赏!鉴于一楼的答案,提醒回答者注意
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![Lebesgue积分题若f是[a,b]上Lebesgue可积函数,证明:当n→∞时,∫(a→b)f(x)|sinnx|dx=2/π*∫(a→b)f(x)dx有能做出来的或者能提供思路的都行啊……好的必有重赏!鉴于一楼的答案,提醒回答者注意](/uploads/image/z/11295089-17-9.jpg?t=Lebesgue%E7%A7%AF%E5%88%86%E9%A2%98%E8%8B%A5f%E6%98%AF%5Ba%2Cb%5D%E4%B8%8ALebesgue%E5%8F%AF%E7%A7%AF%E5%87%BD%E6%95%B0%2C%E8%AF%81%E6%98%8E%EF%BC%9A%E5%BD%93n%E2%86%92%E2%88%9E%E6%97%B6%2C%E2%88%AB%EF%BC%88a%E2%86%92b%EF%BC%89f%28x%29%7Csinnx%7Cdx%3D2%2F%CF%80%2A%E2%88%AB%EF%BC%88a%E2%86%92b%EF%BC%89f%28x%29dx%E6%9C%89%E8%83%BD%E5%81%9A%E5%87%BA%E6%9D%A5%E7%9A%84%E6%88%96%E8%80%85%E8%83%BD%E6%8F%90%E4%BE%9B%E6%80%9D%E8%B7%AF%E7%9A%84%E9%83%BD%E8%A1%8C%E5%95%8A%E2%80%A6%E2%80%A6%E5%A5%BD%E7%9A%84%E5%BF%85%E6%9C%89%E9%87%8D%E8%B5%8F%21%E9%89%B4%E4%BA%8E%E4%B8%80%E6%A5%BC%E7%9A%84%E7%AD%94%E6%A1%88%EF%BC%8C%E6%8F%90%E9%86%92%E5%9B%9E%E7%AD%94%E8%80%85%E6%B3%A8%E6%84%8F)
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