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If $f\\in L^'^{\\,p}$ such that $f$ is the distributional derivative of $F\\in L^p$ then the integral is defined as $\\int^\\infty_{-\\infty} fG=-\\int^\\infty_{-\\infty} F(x)g(x)\\,dx$, where $g\\in L^q$, $G(x)= \\int_0^x g(t)\\,dt$ and $1/p+1/q=1$. A norm is $\\lVert f\\rVert'_p=\\lVert F\\rVert_p$. The spaces $L^'^{\\,p}$ and $L^p$ are isometrically isomorphic. 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Here, $L^p$ is with respect to Lebesgue measure on the real line. If $f\\in L^'^{\\,p}$ such that $f$ is the distributional derivative of $F\\in L^p$ then the integral is defined as $\\int^\\infty_{-\\infty} fG=-\\int^\\infty_{-\\infty} F(x)g(x)\\,dx$, where $g\\in L^q$, $G(x)= \\int_0^x g(t)\\,dt$ and $1/p+1/q=1$. A norm is $\\lVert f\\rVert'_p=\\lVert F\\rVert_p$. The spaces $L^'^{\\,p}$ and $L^p$ are isometrically isomorphic. 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