2

I have such code:

\begin{equation*}
        max_X (min_{\vec{Y}} F(X, \vec{Y})) = sup_{X} (inf_{\vec{Y}} F(X, \vec{Y})) = \Gamma_1, \newline
        min_{\vec{Y}} (max_X F(X, \vec{Y})) = inf_{\vec{Y}} (sup_{X} F(X, \vec{Y})) = \Gamma_2        
    \end{equation*}

How I set a break line? \\ doesn't work too.

2

For example, gather* can be used instead of equation* with package amsmath:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{gather*}
  \max\nolimits_X \min\nolimits_{\vec{Y}} F(X, \vec{Y})) =
  \sup\nolimits_{X} (\inf\nolimits_{\vec{Y}} F(X, \vec{Y})) = \Gamma_1, \\
  \min\nolimits_{\vec{Y}} (\max\nolimits_X F(X, \vec{Y})) =
  \inf\nolimits_{\vec{Y}} (\sup\nolimits_{X} F(X, \vec{Y})) = \Gamma_2
\end{gather*}
\end{document}

Result

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