Answer by Martín-Blas Pérez Pinilla for Why is $L^2$ function Hilbert space...
A $L^2$-Riemann Cauchy sequence of $L^2$-Riemann functions can have a nonintegrable limit (see the example of David Mitra).In general, The Riemann integral behaves much worse that the Lebesge integral....
View ArticleWhy is $L^2$ function Hilbert space not defined for Riemann Integral
The space of square Lebesgue integrable functions is said to be a Hilbert space. Why is if the integral is Riemann then this is not a Hilbert space? In other words, why not the space of Riemann square...
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