bham10246
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Coming up with counterexamples is hard. So to prove or not to prove, that depends if there exists a counterexample.
Question 1 has been ANSWERED!: If f has a bounded variation on [a,b], then is it true that f is of Riemann integration on [a,b]?
Question 2 has been ANSWERED!: Is it true that L^1(\mathbb{R}) \cap L^3(\mathbb{R}) \subseteq L^2(\mathbb{R})?
Question 3. Is it true that
\cap_{1 \leq p<\infty} \: L^{p}(\mathbb{R},m) \subseteq L^{\infty}(\mathbb{R},m) where m denotes Lebesgue measure on \mathbb{R}.
Thank you.
Question 1 has been ANSWERED!: If f has a bounded variation on [a,b], then is it true that f is of Riemann integration on [a,b]?
Question 2 has been ANSWERED!: Is it true that L^1(\mathbb{R}) \cap L^3(\mathbb{R}) \subseteq L^2(\mathbb{R})?
Question 3. Is it true that
\cap_{1 \leq p<\infty} \: L^{p}(\mathbb{R},m) \subseteq L^{\infty}(\mathbb{R},m) where m denotes Lebesgue measure on \mathbb{R}.
Thank you.
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