Is it true that $L_\infty[0;1] \subset L_1[0;1]$ ? How can I prove it?
If $f \in L_\infty[0;1]$, then it's essentially bounded, then we can change $f$ on a zero-measure set and get a bounded on $[0;1]$ function which must be Lebesgue-integrable? Is it true?