I read that: "There's an analogy between the completion of rational numbers by real numbers and the completion of Riemann integrable functions by Lebesgue integrable functions".
Can someone elaborate on that a little bit?
2026-04-02 06:22:28.1775110948
Completion of R-integrable functions by L-integrable functions
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Both are examples of the completion of a metric space. In the case of the rational numbers and reals, the metric is $d(x,y) = |x-y|$. In the case of integration on $[a,b]$, it's $d(x,y) = \int_a^b |x(t) - y(t)|\; dt$.