How do you fit my long equation in my page?

I put this long equation in latex in several lines however when I put Latex into PDF the equation did not appear all. Can I help me?

$$\label{eq:20} \begin{split} \{T_{1} \in (x_{1},x_{1}+h_{1}],\dots,T_{n} \in (x_{n},x_{n}+h_{n}], N(t)=n\} = \\ &\{N(0,x_{1}]=0, N(x_{1},x_{1}+h_{1}] = 1, N(x_{1}+h_{1},x_{2}]=0, \\ & N(x_{2}, x_{2}+h_{2}]=1,\dots, N(x_{n-1}+h_{n-1},x_{n}]=0, \\ & N(x_{n},x_{n}+h_{n}]=1, N(x_{n}+h_{n},t]=0\} \end{split}$$


In PDF:

You need an & in the first line. Instead, I propose one of these two solutions, based of the \MoveEqLeft from mathtools , and the \fleqn environment from nccmath:

\documentclass{article}
\usepackage{mathtools, nccmath}

\begin{document}

Some text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text.

$$\label{eq:20} \begin{split} \MoveEqLeft[3] \{T_{1} \in (x_{1},x_{1}+h_{1}],\dots,T_{n} \in (x_{n},x_{n}+h_{n}], N(t)=n\} = \\ &\{N(0,x_{1}]=0, N(x_{1},x_{1}+h_{1}] = 1, N(x_{1}+h_{1},x_{2}]=0, \\ & N(x_{2}, x_{2}+h_{2}]=1,\dots, N(x_{n-1}+h_{n-1},x_{n}]=0, \\ & N(x_{n},x_{n}+h_{n}]=1, N(x_{n}+h_{n},t]=0\} \end{split}$$
\bigskip

\begin{fleqn}
\begin{aligned} & \mathrlap{\{T_{1} \in (x_{1},x_{1}+h_{1}]\dots,T_{n} \in (x_{n},x_{n}+h_{n}], N(t)=n\} = }\hspace{4em} & & & &\ \\ & & & \{N(0,x_{1}]=0, N(x_{1},x_{1}+h_{1}] = 1, N(x_{1}+h_{1},x_{2}]=0,\\ & & & N(x_{2}, x_{2}+h_{2}]=1,\dots, N(x_{n-1}+h_{n-1},x_{n}]=0, \\ & & & N(x_{n},x_{n}+h_{n}]=1, N(x_{n}+h_{n},t]=0\} \end{aligned}
\end{fleqn}

\end{document}


I suggest to move the = sign to the second line and to align right of the brace, so to emphasize that the items are in the set description. Making the braces a bit larger may help.

\documentclass[a4paper,12pt]{report}
\usepackage{amsmath, mathtools}

\begin{document}

$$\label{eq:20} \begin{split} \MoveEqLeft[4] \bigl\{ T_{1} \in (x_{1},x_{1}+h_{1}],\dots,T_{n} \in (x_{n},x_{n}+h_{n}], N(t)=n \bigr\} \\ =\bigl\{ & N(0,x_{1}]=0, N(x_{1},x_{1}+h_{1}] = 1, N(x_{1}+h_{1},x_{2}]=0, \\ & N(x_{2}, x_{2}+h_{2}]=1,\dots, N(x_{n-1}+h_{n-1},x_{n}]=0, \\ & N(x_{n},x_{n}+h_{n}]=1, N(x_{n}+h_{n},t]=0 \bigr\} \end{split}$$

\end{document}