定义函数R(x)、g(x) R(x)= 1,x=0 1/q,x=p/q,q>0,p与q互素 0,x=无理数 g(x)= 1,x=有理数 0,x=无理数 书上说,R(x)在任意有限区间[a,b]上可积,而g(x)在[0,1]上不可积 我觉得这两个函数差别不大,不理解书上的结论.
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![定义函数R(x)、g(x) R(x)= 1,x=0 1/q,x=p/q,q>0,p与q互素 0,x=无理数 g(x)= 1,x=有理数 0,x=无理数 书上说,R(x)在任意有限区间[a,b]上可积,而g(x)在[0,1]上不可积 我觉得这两个函数差别不大,不理解书上的结论.](/uploads/image/z/11123656-16-6.jpg?t=%E5%AE%9A%E4%B9%89%E5%87%BD%E6%95%B0R%28x%29%E3%80%81g%28x%29+R%28x%29%3D+1%2Cx%3D0+1%2Fq%2Cx%3Dp%2Fq%2Cq%3E0%2Cp%E4%B8%8Eq%E4%BA%92%E7%B4%A0+0%2Cx%3D%E6%97%A0%E7%90%86%E6%95%B0+g%28x%29%3D+1%2Cx%3D%E6%9C%89%E7%90%86%E6%95%B0+0%2Cx%3D%E6%97%A0%E7%90%86%E6%95%B0+%E4%B9%A6%E4%B8%8A%E8%AF%B4%2CR%28x%29%E5%9C%A8%E4%BB%BB%E6%84%8F%E6%9C%89%E9%99%90%E5%8C%BA%E9%97%B4%5Ba%2Cb%5D%E4%B8%8A%E5%8F%AF%E7%A7%AF%2C%E8%80%8Cg%28x%29%E5%9C%A8%5B0%2C1%5D%E4%B8%8A%E4%B8%8D%E5%8F%AF%E7%A7%AF+%E6%88%91%E8%A7%89%E5%BE%97%E8%BF%99%E4%B8%A4%E4%B8%AA%E5%87%BD%E6%95%B0%E5%B7%AE%E5%88%AB%E4%B8%8D%E5%A4%A7%2C%E4%B8%8D%E7%90%86%E8%A7%A3%E4%B9%A6%E4%B8%8A%E7%9A%84%E7%BB%93%E8%AE%BA.)
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