## Open and closed set

4 minute read

Definition 3.1.1 $E$ is a subset of $\mathbb{R}$. $p\in E$ is an interior point of $E$ if there is $\epsilon >0$ such that $N_{\epsilon} (p) \subset E$. ...

## Cauchy Sequence

6 minute read

Definition Let $$\{p_n\}_{n=1}^\infty$$ be a sequence in $\mathbb{R}$. The sequence is a Cauchy sequence if $\forall \epsilon >0, \exists N\in \mathbb{N}$...

## Fundamental Theorem of Linear Algebra

5 minute read

Notation Let $$\mathfrak{B}=\{\mathbf{v}_1, \ldots, \mathbf{v}_n \} \text{ is a basis for } V.$$ Define a function \([\cdot]_{\mathfrak{B}}:V \rightarr...

## Distribution Function

2 minute read

Distribution Function Let $X$ be a random variable on $(\mathbb{R}, \mathcal{B}(\mathbb{R}), \mu)$. The distribution function (cumulative distribution functi...

## Random Variable

less than 1 minute read

Measurable function Let $(E, \mathcal{E})$ and $(F, \mathcal{F})$ be measurable spaces where $E,F,$ are sets and $\mathcal{E}$ and $\mathcal{F}$ are \$\sigma...