True or false: if $f$ is an integrable function on $[a,b]$, then the set where the function is continuous, is dense in $[a,b]$.
Observation: the function $f$ is Riemann-integrable.
2026-03-29 23:24:51.1774826691
If $f(x)$ is an integrable function in $[a,b],$ then the set where the function is continuous, is dense in $[a,b]$?
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Hint: Use Lebesgue's integrability condition. Notice that a subset of $[a,b]$ which is almost equal to it (its Lebesgue measure is $b-a$) is dense in it.