# Sets

 $\emptyset$ empty set $\N, \N^+$ Natural numbers include/excluding 0 respectively $\R$ real numbers $\bar \R$ $\R \cup \{-\infty, \infty\}$ $[n]$ $\{1,2,\ldots,n\}$ $2^A$ powerset of $A$ $A^*$ set of finite sequences over $A$ $B_2^d$ $d$-dimensional unit ball, $\{x \in \R^d : \norm{x}_2 \leq 1\}$ $\cP_d$ $d$-dimensional probability simplex, $\{x \in [0,1]^{d+1} : \norm{x}_1 = 1\}$ $\cP(A)$ set of distributions over $A$ $\borel(A)$ Borel $\sigma$-algebra on $A$