27 Is a function Lipschitz if and only if its derivative is bounded? 13 Proofs of AM-GM inequality 13 $C(X)$ is separable when $X$ is compact? 4 Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$ 4 Is $\lim_n (1/n)\log(x_n)=\lim_n(1/n)\log(x_n+1)$?

### Reputation (1,865)

 +10 Can ${L^{1}}(G)$ be a $C^{*}$-algebra? +20 Is a function Lipschitz if and only if its derivative is bounded? +10 Proofs of AM-GM inequality +10 $C(X)$ is separable when $X$ is compact?

### Questions (30)

 8 Can ${L^{1}}(G)$ be a $C^{*}$-algebra? 5 Find the minimum value of $A=\frac{2-a^3}{a}+\frac{2-b^3}{b}+\frac{2-c^3}{c}$ 5 Convergence of a sum of random variables 5 Equivalence between conditions for convergence 4 Commutativity criteria for $C^*$-algebras

### Tags (78)

 29 calculus × 5 17 inequality × 9 27 real-analysis × 8 13 means 27 lipschitz-functions 13 alternative-proof 27 derivatives 13 a.m.-g.m.-inequality 25 functional-analysis × 11 8 integration × 5

### Bookmarks (13)

 35 On the inequality $\int_{-\infty}^{+\infty}\frac{(p'(x))^2}{(p'(x))^2+(p(x))^2}\,dx \le n^{3/2}\pi.$ 13 About the Polya-Knopp-like inequality $\sum_{k=1}^{n}\frac{k^2}{a^2_{1}+\cdots+a^2_{k}}\le\left(\frac{1}{a_{1}}+\cdots+\frac{1}{a_{n}}\right)^2$ 11 Conditional expectation $\mathbb E\left(\exp\left(\int_0^tX_sdB_s\right) \mid \mathcal F_t^X\right)$ 10 Prove the time inversion formula is brownian motion 10 Change of variables for stochastic integral

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