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> Let us recall that the {{{equation}}} (or {{{equation*}}}) environment is used for typesetting a single equation in a separate line with an automatically generated number (the latter one omits the number of the formula).
> For equations that do not fit on a single line use the environments {{{align}}} ({{{align*}}}) or {{{multline}}} ({{{multline*}}}). Since the names of the commands speak for themselves, we shall pass to the following example:
> <LaTeX-source>
> \documentclass{article}
> \usepackage{amsmath}
> \begin{document}
> Using H\"older inequality we obtain
> \begin{align}
> \|f + g\|_2^2 & = \int |f + g|^2 \textup d\mu \leq \int (|f| + |g|)|f + g| \textup d\mu \\
> & = \int |f||f + g| \textup d\mu +\int |g||f + g| \textup d\mu \\
> & \leq \biggl[ \biggl( \int |f|^2 \textup d\mu \biggr)^{1/2} + \biggl(\int |g|^2 \textup d\mu \biggr)^{1/2} \biggr] \biggl(\int |f + g|^2 \textup d\mu \biggr)^{1/2}\\
> & = \bigl(\|f\|_2 + \|g\|_2 \bigr)\frac{\|f + g\|_2^2}{\|f + g\|_2}.
> \end{align}
> \end{document}
> </LaTeX-source>
> The command which allows us to omit a number in a line is {{{\notag}}} (written at the end of the line, but before the "next line" command {{{\\}}}):
> <LaTeX-source>
> \documentclass{article}
> \usepackage{amsmath}
> \begin{document}
> Using H\"older inequality we obtain
> \begin{align}
> \|f + g\|_2^2 & = \int |f + g|^2 \textup d\mu \leq \int (|f| + |g|)|f + g| \textup d\mu \\
> & = \int |f||f + g| \textup d\mu +\int |g||f + g| \textup d\mu \notag \\
> & \leq \biggl[ \biggl( \int |f|^2 \textup d\mu \biggr)^{1/2} + \biggl(\int |g|^2 \textup d\mu \biggr)^{1/2} \biggr] \biggl(\int |f + g|^2 \textup d\mu \biggr)^{1/2}\\
> & = \bigl(\|f\|_2 + \|g\|_2 \bigr)\frac{\|f + g\|_2^2}{\|f + g\|_2}. \notag
> \end{align}
> \end{document}
> </LaTeX-source>
> Note that when you use {{{align}}} environment, each line gets a number. If you would like the whole formula to be numbered as a one equation, you have to use {{{split}}} environment. (Remember that {{{split}}} is intended to be used only inside other "displayed equation" structures.)
> <LaTeX-source>
> \documentclass{article}
> \usepackage{amsmath}
> \begin{document}
> Using H\"older inequality we obtain
> \begin{align}
> \begin{split}
> \|f + g\|_2^2 & = \int |f + g|^2 \textup d\mu \leq \int (|f| + |g|)|f + g| \textup d\mu \\
> & = \int |f||f + g| \textup d\mu +\int |g||f + g| \textup d\mu \\
> & \leq \biggl[ \biggl( \int |f|^2 \textup d\mu \biggr)^{1/2} + \biggl(\int |g|^2 \textup d\mu \biggr)^{1/2} \biggr] \biggl(\int |f + g|^2 \textup d\mu \biggr)^{1/2}\\
> & = \bigl(\|f\|_2 + \|g\|_2 \bigr)\frac{\|f + g\|_2^2}{\|f + g\|_2}.
> \end{split}
> \end{align}
> \end{document}
> </LaTeX-source>
> The second environment we are going to talk about is {{{multline}}}. The first line of a {{{multline}}} will be at the left margin and the last line at the right margin. Any additional lines in between will be centered within the display width.
> <LaTeX-source>
> \documentclass{article}
> \usepackage{amsmath}
> \begin{document}
> Using H\"older inequality we obtain
> \begin{multline}
> \|f + g\|_2^2 = \int |f||f + g| \textup d\mu +\int |g||f + g| \textup d\mu \\
> \leq \biggl[ \biggl( \int |f|^2 \textup d\mu \biggr)^{1/2} + \biggl(\int |g|^2 \textup d\mu \biggr)^{1/2} \biggr] \biggl(\int |f + g|^2 \textup d\mu \biggr)^{1/2}
> \end{multline}
> from which follows our assertion.
> \end{document}
> </LaTeX-source>
> Since {{{multline}}} produces only one number (and thus none of the invidual lines should be marked with {{{\notag}}}), we cannot use the {{{split}}} environment inside it.
Let us recall that the equation (or equation*) environment is used for typesetting a single equation in a separate line with an automatically generated number (the latter one omits the number of the formula).
For equations that do not fit on a single line use the environments align (align*) or multline (multline*). Since the names of the commands speak for themselves, we shall pass to the following example:
\documentclass{article} \usepackage{amsmath} \begin{document} Using H\"older inequality we obtain \begin{align} \|f + g\|_2^2 & = \int |f + g|^2 \textup d\mu \leq \int (|f| + |g|)|f + g| \textup d\mu \\ & = \int |f||f + g| \textup d\mu +\int |g||f + g| \textup d\mu \\ & \leq \biggl[ \biggl( \int |f|^2 \textup d\mu \biggr)^{1/2} + \biggl(\int |g|^2 \textup d\mu \biggr)^{1/2} \biggr] \biggl(\int |f + g|^2 \textup d\mu \biggr)^{1/2}\\ & = \bigl(\|f\|_2 + \|g\|_2 \bigr)\frac{\|f + g\|_2^2}{\|f + g\|_2}. \end{align} \end{document}
The command which allows us to omit a number in a line is \notag (written at the end of the line, but before the “next line” command \\):
\documentclass{article} \usepackage{amsmath} \begin{document} Using H\"older inequality we obtain \begin{align} \|f + g\|_2^2 & = \int |f + g|^2 \textup d\mu \leq \int (|f| + |g|)|f + g| \textup d\mu \\ & = \int |f||f + g| \textup d\mu +\int |g||f + g| \textup d\mu \notag \\ & \leq \biggl[ \biggl( \int |f|^2 \textup d\mu \biggr)^{1/2} + \biggl(\int |g|^2 \textup d\mu \biggr)^{1/2} \biggr] \biggl(\int |f + g|^2 \textup d\mu \biggr)^{1/2}\\ & = \bigl(\|f\|_2 + \|g\|_2 \bigr)\frac{\|f + g\|_2^2}{\|f + g\|_2}. \notag \end{align} \end{document}
Note that when you use align environment, each line gets a number. If you would like the whole formula to be numbered as a one equation, you have to use split environment. (Remember that split is intended to be used only inside other “displayed equation” structures.)
\documentclass{article} \usepackage{amsmath} \begin{document} Using H\"older inequality we obtain \begin{align} \begin{split} \|f + g\|_2^2 & = \int |f + g|^2 \textup d\mu \leq \int (|f| + |g|)|f + g| \textup d\mu \\ & = \int |f||f + g| \textup d\mu +\int |g||f + g| \textup d\mu \\ & \leq \biggl[ \biggl( \int |f|^2 \textup d\mu \biggr)^{1/2} + \biggl(\int |g|^2 \textup d\mu \biggr)^{1/2} \biggr] \biggl(\int |f + g|^2 \textup d\mu \biggr)^{1/2}\\ & = \bigl(\|f\|_2 + \|g\|_2 \bigr)\frac{\|f + g\|_2^2}{\|f + g\|_2}. \end{split} \end{align} \end{document}
The second environment we are going to talk about is multline. The first line of a multline will be at the left margin and the last line at the right margin. Any additional lines in between will be centered within the display width.
\documentclass{article} \usepackage{amsmath} \begin{document} Using H\"older inequality we obtain \begin{multline} \|f + g\|_2^2 = \int |f||f + g| \textup d\mu +\int |g||f + g| \textup d\mu \\ \leq \biggl[ \biggl( \int |f|^2 \textup d\mu \biggr)^{1/2} + \biggl(\int |g|^2 \textup d\mu \biggr)^{1/2} \biggr] \biggl(\int |f + g|^2 \textup d\mu \biggr)^{1/2} \end{multline} from which follows our assertion. \end{document}
Since multline produces only one number (and thus none of the invidual lines should be marked with \notag), we cannot use the split environment inside it.