### Questions (77)

 5 Given two biholomorphic maps such that $f(z_0)=g(z_0)=0$, prove there exists $c$ such that $f(z)=cg(z)$ 3 If $f_n\rightarrow f$ uniformly on compact subsets $\Omega$ and $f$ is not constant, prove $f(\Omega)\subseteq \Omega$ 3 Prove that there exists $h\in V$, such that $|f'(\frac{1}{2})|\leq|h'(\frac{1}{2})|$ for all $f\in V$. 3 $f$ is integrable implies $F(x)$ is bounded variation. 3 Show that $\displaystyle (1-|z|)|f'(z)|\leq\sup_{z\in D}|f(z)|$ for all $z\in D$

### Reputation (551)

 +5 $m$ minimizes $E(|X-a|)$ over $a\in R$ if and only if $m$ is a median for $X$. +5 Linearity of Fourier transformation. +5 $f$ is integrable implies $F(x)$ is bounded variation. +5 Prove $\rho(id)=I$ and $\rho(s^{-1})=\rho(s)^{-1}$

### Answers (2)

 2 True or False $Re f(z)>0$ 0 Question regarding probability.

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 2 complex-analysis × 35 0 measure-theory × 8 0 real-analysis × 14 0 general-topology × 7 0 finite-groups × 12 0 sylow-theory × 6 0 abstract-algebra × 10 0 representation-theory × 6 0 group-theory × 10 0 lebesgue-integral × 5

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