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    Lebesgue Integration

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    For what values of a in R (real numbers) is the function (1+x^2)^a in L^2

    NOTE: let L^2 be like in Lebesgue integration where the set of all measurable functions that are square-integrable forms a Hilbert space, the so-called L2 space.

    keywords: integration, integrates, integrals, integrating, double, triple, multiple, riemann integrable, lebesgue integrable

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    Let . Let L= .
    1. If a=0, f(x)=1 is obviously not integrable
    2. if a>0, the function is Riemann-integrable in every interval [-R,R]. According to ...

    Solution Summary

    Lebesgue integrability and Riemann integrability are investigated. The solution is detailed and well presented.