LaTeX Forum

\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{align*} 
 C_{T_R}(\bar{x},\bar{y})
  & = \left\{ 
    d \in \mathbb{R}^{2n} :
    \exists \left\{(x^k,y^k)\right\}_{k=1}^\infty \subseteq T_R,
    \; \exists \{  t_k\}_{k=1}^\infty 
    \subseteq \mathbb{R}_{+}\setminus \{ 0\},
    \right.\\  
%
  &\qquad\left.
    \lim\limits_{k\rightarrow \infty}{t_k} = 0,
    \;d= \lim\limits_{k \rightarrow \infty}{\frac{1}{t_k}
    \left((x^k,y^k)-(\bar{x},\bar{y})\right)} \right\} 
\end{align*} 
%
oder besser mit gleich großen äußeren Klammern
%
\begin{align*} 
 C_{T_R}(\bar{x},\bar{y})
  & = \bigg\{
    d \in \mathbb{R}^{2n} :
    \exists \left\{(x^k,y^k)\right\}_{k=1}^\infty \subseteq T_R,
    \; \exists \{  t_k\}_{k=1}^\infty 
    \subseteq \mathbb{R}_{+}\setminus \{ 0\},
    \\ 
%
  &\qquad
    \lim\limits_{k\rightarrow \infty}{t_k} = 0,
    \;d= \lim\limits_{k \rightarrow \infty}{\frac{1}{t_k}
    \left((x^k,y^k)-(\bar{x},\bar{y})\right)}
    \bigg\} 
\end{align*} 
\end{document}

\begin{align*}
C_{T_R}(\bar{x},\bar{y}) = \left\lbrace d \in \mathbb{R}^{2n} : \exists  \lbrace(x^k,y^k)\rbrace_{k=1}^\infty \subseteq T_R, \; \exists \lbrace  t_k\rbrace_{k=1}^\infty \subseteq \mathbb{R}_{+}\setminus \lbrace 0\rbrace, \;  \lim\limits_{k\rightarrow \infty}{t_k} = 0, \;d= \lim\limits_{k \rightarrow \infty}{\frac{1}{t_k}((x^k,y^k)-(\bar{x},\bar{y}))} \right\rbrace
\end{align*}

\begin{align*}
C_{T_R}(\bar{x},\bar{y}) = \left\lbrace d \in \mathbb{R}^{2n} : \exists  \lbrace(x^k,y^k)\rbrace_{k=1}^\infty \subseteq T_R, \; \exists \lbrace  t_k\rbrace_{k=1}^\infty \subseteq \mathbb{R}_{+}\setminus \lbrace 0\rbrace, \right} \\ \left{ \lim\limits_{k\rightarrow \infty}{t_k} = 0, \;d= \lim\limits_{k \rightarrow \infty}{\frac{1}{t_k}((x^k,y^k)-(\bar{x},\bar{y}))} \right\rbrace
\end{align*}