Suprema proof: Prove $\sup(f+g)\leq \sup f+\sup g$
10859
Prove $\sup(f+g) \le \sup f + \sup g$
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
149664
Norm is sup of inner products (proof).
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
121504
Supremum of a product measurable function...
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
146480
Example of $\deg(fg)<\deg(f)+\deg(g)$
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
69184
Proof that absolute value of supremum equals suprememum of absolute value
100565
Property of sup of a set of numbers
96848
Prove: $\limsup_{n\to\infty} (a_n)\leq \sup(a_n)_{n=1}^\infty$
88064
Prove: $a_n \leq b_n \implies \limsup a_n \leq \limsup b_n$
77026
Proof with inequalities
107894
Inequality involving the sup of a function and its first and second derivatives
81203
Supremum and infimum of sets