Show that $L^1\subsetneq (L^\infty)^*$
118272
Show that $L^1$ is strictly contained in $(L^\infty)^*$
55266
Prove that $(n+1)^{n-1}<n^n$
146839
Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball
145772
Proving $\liminf_{n\to\infty}(-a_n)=-\limsup_{n\to\infty}(a_n)$
70746
Proving that $(x_n)_{n=1}^{\infty}$ is a Cauchy sequence.
1332
Pointwise convergence and convergence of integrals implies $L^1$ convergence
68153
How to show that $L^p$ spaces are nested?
83959
If $f \in L_p \cap L_q$, $1 \leq p < r < q < \infty$ then $f \in L_r$.
966
Show that $\lim_{n\rightarrow \infty} \sqrt[n]{c_1^n+c_2^n+\ldots+c_m^n} = \max\{c_1,c_2,\ldots,c_m\}$
137640
Proof that $\sum_{1}^{\infty} \frac{1}{n^2} <2$
73696
Given $(a_n)$ with $a_n \geq a_{n+1} \geq 0$ show that if $\sum \sqrt{a_n a_{n+1}} < \infty \implies \sum a_n < \infty$
110526
Why is $l^\infty$ not separable?
149564
Showing that a function is in $L^1$
13561
Show: $E(|X|)\leqslant\liminf_{n\to\infty} E(|X_n|)$
129331
Prove that $|x^p - y^p| \le p|x-y|(x^{p-1} + y^{p-1})$ provided that $1 \le p \lt \infty$ and $x, y \ge 0$
47668
Show that $lim_{n \rightarrow \infty}m(O_n)=m(E)$ when $E$ is compact.
81302
Showing that $a_n \in \ell^{\infty}$