LaTeX Forum

\documentclass[12pt,leqno]{scrartcl}
\usepackage[ngerman]{babel}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb,amsmath,amsfonts}
\usepackage{mathtools}

\begin{document} 

\begin{flalign*}
\overline{P}\{k_l&>0 \,\,\text{aber}\,\, Z_{N_{k_i}}>0 \,\,\text{für}\,\, i=1, \dots,l\}\\
&= \sum_{r=1}^{k-1}\overline{P}\{Z_{N_k}>0, k_1=r\}P\{k_l>0
\,\,\text{aber}\,\, Z_{N_{k_i}}>0 \,\,\text{für} i=1, \dot,l|Z_{N_k}>0, k_1=r\}\\
&\leq (1-d)\max_{1\le r<k}\overline{P}\{k_l>0\,\,\text{aber}\,\, Z_{N_{k_i}}>0\,\,\text{für} i=1,\dots,l|Z_{N_k}>0, k_1=r\}\\
&= (1-d)\max_{1\le r<k}\overline{P}\{k_l>0\,\,\text{aber}\,\,Z_{N_{k_i}}<0\,\,\text{für}\,\,i=1.\dots,l|\sum_{s=N_r}^{N_k-1} Z_{s,N_k}>0\\
\text{aber}\,\,\sum_{s=N_{r+1}}^{N_k-1} Z_{s,N_k}=0\}\\
&\leq \dots \leq\\
&\leq (1-d)^{l+1}
\end{flalign*}


\end{document}

\documentclass[12pt,leqno]{scrartcl}
\usepackage[ngerman]{babel}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb,amsmath,amsfonts}
\usepackage{mathtools}

\begin{document}

\begin{align*}
  \begin{split}
    &\limsup P \Bigl\{ n^{-1}(T_n-2C_1\mu^{-1}nD(n\mu^{-1})\le x \Bigr\}\\
    &\qquad = \limsup P \left\{ n^{-1} n+2\sum_{t=0}^{n-1} Z_t-2C_1\mu^{-1}nD(n\mu^{-1})\le x \right\}\\
    &\qquad \le L \left(\frac{1}{2}\mu(x-1) \right)
  \end{split}
\end{align*}

\begin{flalign*}
  a &= b &\\
  &= c &\\
  &\leq d &
\end{flalign*}

\end{document} 

\documentclass[12pt,leqno]{scrartcl}
\usepackage[ngerman]{babel}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb,amsmath,amsfonts}
\usepackage{mathtools}

\begin{document}

\begin{align*}
\limsup P\{n^{-1}(T_n&-2C_1\mu^{-1}nD(n\mu^{-1})\le x\}\\
&= \limsup P\{n^{-1}(n+2\sum_{t=0}^{n-1} Z_t-2C_1\mu^{-1}nD(n\mu^{-1})\le x\}\\
&\le L\Big(\frac{1}{2}\mu(x-1)\Big)
\end{align*}

\end{document}
 

\documentclass[12pt,leqno]{scrartcl}
\usepackage[ngerman]{babel}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amssymb,amsmath,amsfonts}
\usepackage{mathtools}

\begin{document}

\begin{eqnarray*}
\limsup P\{n^{-1}(T_n-2C_1\mu^{-1}nD(n\mu^{-1})\le x\}\\
&=& \limsup P\{n^{-1}(n+2\sum_{t=0}^{n-1} Z_t-2C_1\mu^{-1}nD(n\mu^{-1})\le x\}\\
&\le& L\Big(\frac{1}{2}\mu(x-1)\Big)
\end{eqnarray*}

\end{document}