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Probability Space

2 minute read

The sample space $\Omega$ is the set of all possible outcomes of an experiment. Points in $\omega \in \Omega$ are outcomes or realizations.

Monotone Sequences

2 minute read

Definition 2.3.1 A sequence \(\{a_n\}\) is said to be (a) monotone increasing if $a_n \leq a_{n+1}$ for all $n\in\mathbb{N}$ (b) monotone decreasing if $a_...

Sequences of real numbers

7 minute read

Theorem 2.1.3 (Triangular inequality) For all $x,y\in \mathbb{R}, \lvert x+y\rvert\leq \vert x\rvert+\vert y\rvert$