# 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 $A$ |