Error Missing $ inserted, Help!

Question

Buen día tengo un trabajo y quiero poner algunas cosas, soy nuevo en esto asi que me surgieron muchas dudas, este es mi codigo:

\documentclass{beamer}
\usepackage[spanish]{babel}
\usetheme{Madrid}
\title{4.2 Funciones Integrables}
\author{J.~Zacarias\inst{} \and P.~Rodr\'iguez\inst{} \and H.~Dom\'inguez \inst{}}
\institute[] % (optional, but mostly needed)
{
  \inst{}%
  Universidad Aut\'onoma de Yucat\'an\\
  Facultad de Matem\'aticas}
\date{Viernes 4 de diciembre de 2015}
\subject{}
\AtBeginSubsection[]
{
  \begin{frame}<beamer>{Funciones Integrables}
    \tableofcontents[currentsection,currentsubsection]
  \end{frame}
}
% Let's get started
\begin{document}
\begin{frame}
  \titlepage
\end{frame}
\begin{frame}{Fundamentos y conceptos b\'asicos de integraci\'on`}
\begin{block}{Definici\'on 4.2.1.}
Sea $f : A \subset \mathbb{R}^n \rightarrow \mathbb{R}\ $acotada .Si $B$ \subset\ A \ $definimos$: \\
 \item 
    \centering $M_B(f)=sup \{f(x) : x\in B\}\\
 \item
    \centering $m_B(f) = inf\{f(x) : x\in B\}
\end{block}
\end{frame}
\end{document}

Answer 1

Your input has some glitches; you are mainly forgetting to balance opening and closing $ for formulas. Here's a part of your code.

\begin{block}{Definici\'on 4.2.1.}
Sea $f : A \subset \mathbb{R}^n \rightarrow \mathbb{R}\ $acotada .Si $B$ \subset\ A \ $definimos$: \\
 \item 
    \centering $M_B(f)=sup \{f(x) : x\in B\}\\
 \item
    \centering $m_B(f) = inf\{f(x) : x\in B\}
\end{block}

1. In general, the closing $ is followed either by a space or punctuation; don't put the space before it.

2. The sentence ending period must be next to the final word

3. A formula contains everything that's math: $B\subset A$

4. Names of common functions such as logarithm, supremum, infimum and so on, should be written in upright font.

5. Don't substitute display math mode with \centering

6. Recall that \centering continues until the end of the current group

Fixed version

\begin{block}{Definici\'on 4.2.1.}
Sea $f\colon A \subset \mathbb{R}^n \rightarrow \mathbb{R}$ acotada.
Si $B \subset A$ definimos:
\begin{gather*}
M_B(f)=sup \{f(x) : x\in B\}\\
m_B(f) = inf\{f(x) : x\in B\}
\end{gather*}
\end{block}