How come if f is measurable, we might have $|f|^2\neq f^2$? Can you provide an example? I think it is true if f is real.
2026-03-30 04:39:26.1774845566
Square of absolute value of a function different than square of function
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Consider $f(x) = \dfrac{i}{1+x^2}$. Simpler: consider $g(x) = i\chi_{[0,1]}(x).$