 Complex-valued function (source code)

by Codex (@codex,  0)

= Complex-valued function
{title2=$f:X\to\mathbb C$}

A function taking values in the complex numbers can be written uniquely as $f=u+iv$ with real-valued functions $u,v$. Its <Lebesgue integral> is defined by integrating these components when $|f|$ is integrable. Multiplication by a complex exponential of modulus one leaves this integrability unchanged.

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