[Tex/LaTex] The curly brace is too big

Question

\documentclass{article}
\begin{document}
\begin{equation*}
P^*(A) = \begin{cases}
1 & \quad \omega_0 \in A, \\
0 & \quad \omega_0 \notin A.
\end{cases}
\end{equation*}
\end{document}

When I used the above code to display a piecewise expression, I got the following:

Clearly, the curly brace appeared in the expression is too big, how can I adjust it so the display is more satisfactory? Thanks in advance.

P.S: My preamble:

\usepackage{setspace} 
\doublespacing
\usepackage[margin = 1.5in]{geometry}
\usepackage{float} 
\usepackage{graphicx}
\usepackage{color} 
\usepackage{amsmath} 
\usepackage{amsfonts} 
\usepackage{amsthm}
\usepackage{bm} 
\usepackage{framed}
\usepackage{verbatim}
\usepackage{natbib}
%\usepackage[symbol*]{footmisc}
\usepackage[stable]{footmisc}
\usepackage{mathtools}
\usepackage{mathrsfs}
\usepackage{amssymb}
\usepackage{hyperref}



\newcommand{\eps}{\varepsilon}
\newcommand{\rational}{\mathbb{Q}}
\newcommand{\real}{\mathbb{R}}
\newcommand{\integer}{\mathbb{Z}}
\newcommand{\nn}{\mathbb{N}}
\newcommand{\complex}{\mathbb{C}}
\newcommand{\Ell}{\mathcal{L}}
\newcommand{\mean}{\mathbb{E}}
\newcommand{\prob}{\mathbb{P}}
\newcommand{\dd}{\mathop{}\!\mathrm{d}}
\newcommand{\overbar}[1]{\mkern 1.5mu\overline{\mkern-1.5mu#1\mkern1.5mu}\mkern 1.5mu}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\diam}{diam\,}
\newcommand{\Riemann}{\mathscr{R}}

\theoremstyle{definition}
\newtheorem{defn}{Definition}[section]
\newtheorem{defns}{Definitions}[section]
\newtheorem{exmp}{Example}[section]

\theoremstyle{plain}
\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}{Lemma}
\newtheorem{prop}{Proposition}
\newtheorem*{cor}{Corollary}

\theoremstyle{remark}
\newtheorem*{rem}{Remark} 

Answer 1

Package amsmath is missing, which defines environments equation* and cases:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
P^*(A) = \begin{cases}
1 & \quad \omega_0 \in A, \\
0 & \quad \omega_0 \notin A.
\end{cases}
\end{equation*}
\end{document}

The brace looks normal sized.

Updated question

The preamble uses

\usepackage{setspace}
\doublespacing

As set, the increased line spacing also affects cases (and array, tabular). Workaround: A local switch to \singlespacing:

\documentclass{article}
\usepackage{setspace}
\doublespacing
\usepackage{amsmath}
\begin{document}
\begin{equation*}
P^*(A) = \begin{cases}
1 & \quad \omega_0 \in A, \\
0 & \quad \omega_0 \notin A.
\end{cases}
\end{equation*}
\begingroup
  \singlespacing
  \begin{equation*}
  P^*(A) = \begin{cases}
  1 & \quad \omega_0 \in A, \\
  0 & \quad \omega_0 \notin A.
  \end{cases}
  \end{equation*}
\endgroup
\end{document}