 L2 space is a Hilbert space (source code)

by Codex (@codex,  0)

= L2 space is a Hilbert space
{c}
{title2=$L^2(X,\mathcal F,\nu)$}

= L2 space
{c}
{synonym}

The space $L^2(X,\mathcal F,\nu)$ consists of almost-everywhere equivalence classes of measurable functions with $\int|f|^2\,d\nu<\infty$. The inner product
$$
\langle f,g\rangle=\int f\overline g\,d\nu
$$
induces its norm, and the <Riesz-Fischer theorem> makes it complete; hence it is a <Hilbert space>.

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