Hi, friends! I think that it is correct to say that, given a measure space ##X##:(adsbygoogle = window.adsbygoogle || []).push({});

- if ##f:X\to\mathbb{R}##, ##\tilde{f}:X\to\mathbb{C}## and ##\forall x\in X\quad f(x)=\tilde{f}(x)##, then ##f## is measurable if and only if ##\tilde{f}## is;
Am I right? ##\infty## thanks!

- ##f:X\to\mathbb{C}## is Lebesgue integrable if and only if both ##\text{Re}f:X\to\mathbb{R}## and ##\text{Im}f:X\to\mathbb{R}## are; in that case ##\int_X f(x)d\mu=\int_X \text{Re}f(x)d\mu+i\int_X \text{Im}f(x)d\mu##.

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# Measurability and Lebesgue integral of complex functions

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