Contents

1. Mathematical Analysis
2. Measure Theory
3. Matrix Analysis
4. Real Analysis
5. Functional Analysis

• Mathematical Analysis

• Measure Theory

1.[2014-08-12] $g$ is a real function on a closed interval $\left[ {a,b} \right]$ and $c \le g\left( x \right) \le d$ where $c,d \ne  \pm \infty $. Let $H = \left\{ {x \in \left( {a,b} \right):g‘\left( x \right){\rm{ ~exists~ and ~}}g‘\left( x \right) \ne 0} \right\}$. If $E \subseteq \left[ {c,d} \right]$ and $m\left( E \right) = 0$ where $m$ is Lebesgue measure, then does $m\left( {{g^{ - 1}}\left( E \right) \cap H} \right) = 0$? How about $c =  - \infty $ & $d = \infty $?

• Matrix Analysis

• Real Analysis

• Functional Analysis