Coming up with counterexamples is hard. So to prove or not to prove, that depends if there exists a counterexample.(adsbygoogle = window.adsbygoogle || []).push({});

Question 1 has been ANSWERED!:If [itex]f[/itex] has a bounded variation on [itex] [a,b] [/itex], then is it true that [itex]f[/itex] is of Riemann integration on [itex][a,b][/itex]?

Question 2 has been ANSWERED!:Is it true that [itex]L^1(\mathbb{R}) \cap L^3(\mathbb{R}) \subseteq L^2(\mathbb{R}) [/itex]?

Question 3.Is it true that

[itex]\cap_{1 \leq p<\infty} \: L^{p}(\mathbb{R},m) \subseteq L^{\infty}(\mathbb{R},m) [/itex] where [itex]m[/itex] denotes Lebesgue measure on [itex]\mathbb{R}[/itex].

Thank you.

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# Coming up with counterexamples in Real Analysis

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