Math Notations
Notations We use upper-case sans serif letters, e.g., $\mathsf{Z}$ to denote random variables with sample spaces denoted as $\mathcal{Z}$. $p_{\mathsf{Z}}$ denote the distribution of $\mathsf{Z}$, which is a propability density function if $\mathsf{Z}$ is continuous. $P_{\mathsf{Z}}$ denotes the probability measure. $\mathcal{P}(\mathcal{Z})$ denotes the set of all probability measures over the Borel σ-algebra on $\mathcal{Z}$. $E[\mathsf{Z}]$ denotes the expectation of $\mathsf{Z}$. Let $(\mathsf{Z}_1,\mathsf{Z}_2,\cdots,\mathsf{Z}_n)$ be $n$ i.i.d. copies of $\mathsf{Z}$. We use $\mathsf{Z}^n$ to denote the sequence $\{\mathsf{Z}_1,\mathsf{Z}_2,\cdots,\mathsf{Z}_n\}$....