= Lp duality on an arbitrary measure space
{c}
{title2=$(L^p)^*\cong L^q,\quad1<p<\infty$}
For conjugate exponents $p,q\in(1,\infty)$, every <bounded linear functional> on an <Lp space> is uniquely $h\mapsto\int hg\,d\mu$ for $g\in L^q$, with functional norm $\|g\|_q$. This holds on arbitrary <measure spaces>. Apply the <Radon-Nikodym theorem> on finite-measure pieces, then use <support localization of an Lp functional> to obtain one global density without assuming sigma-finiteness of the entire measure.
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