I am looking for an environment that align equations as the following example (from the book by Dunford & Schwartz)

I mean main equation content is centered and variable, quantifier push to the right. note that align with a single equation does not give me the desired result since $f\in F$ is not completely pushed to the right and the integral is not centered.

Well, any idea?

Thanks.

Replay

You can do it with flalign, but I consider it quite bad style. I suggest other two possibilities, the final one is what I'd prefer.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath}
\begin{document}
\noindent % just for emulating the original
conditions guaranteeing that
\begin{flalign*}
&& \int_{0}^{1} f(s)\phi_{n}(s)\,ds \to 0, &&& f\in F.
\end{flalign*}
Where the functions $f$ and $\phi_{n}$ are taken to be
in certain preassigned blah blah blah blah blah
\bigskip
\noindent % just for emulating the original
conditions guaranteeing that
\begin{equation*}
\int_{0}^{1} f(s)\phi_{n}(s)\,ds \to 0,\qquad f\in F,
\end{equation*}
where the functions $f$ and $\phi_{n}$ are taken to be
in certain preassigned blah blah blah blah blah
\bigskip
\noindent % just for emulating the original
conditions guaranteeing that, for $f\in F$,
\begin{equation*}
\int_{0}^{1} f(s)\phi_{n}(s)\,ds \to 0,
\end{equation*}
where the functions $f$ and $\phi_{n}$ are taken to be
in certain preassigned blah blah blah blah blah
\end{document}

I fixed the obvious typo (dx should clearly be ds) and, in the final two examples, removed the grammatically wrong period before “where”.

The main formula can be centered by making the condition to have zero width (but this wouldn't work with wider main formulas).

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,mathtools}
\begin{document}
\noindent % just for emulating the original
conditions guaranteeing that
\begin{flalign*}
&& \int_{0}^{1} f(s)\phi_{n}(s)\,ds \to 0{,} &&& \mathllap{f\in F}.
\end{flalign*}
Where the functions $f$ and $\phi_{n}$ are taken to be
in certain preassigned blah blah blah blah blah
\bigskip
\noindent % just for emulating the original
conditions guaranteeing that
\begin{equation*}
\int_{0}^{1} f(s)\phi_{n}(s)\,ds \to 0{,}\mathrlap{\qquad f\in F,}
\end{equation*}
where the functions $f$ and $\phi_{n}$ are taken to be
in certain preassigned blah blah blah blah blah
\bigskip
\noindent % just for emulating the original
conditions guaranteeing that, for $f\in F$,
\begin{equation*}
\int_{0}^{1} f(s)\phi_{n}(s)\,ds \to 0,
\end{equation*}
where the functions $f$ and $\phi_{n}$ are taken to be
in certain preassigned blah blah blah blah blah
\end{document}

These variants allow to have the main equation centred between the margins.

The last solution, in case of consecutive equations with quantifiers towards the right margin,lets all quantifiers begin at the same point on the page, the widest ending exactly at the right margin:

\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[lf]{MinionPro}
\usepackage[showframe]{geometry}
\usepackage{mathtools, eqparbox}
\begin{document}
\noindent
conditions guaranteeing that
\begin{align*}
& & ∫_0¹f(s)\phi_n(s)\,d\mkern1mu s & \to 0 & & \mathrlap{f ∈ F. }
\end{align*}
\begin{align*}
& & ∫_0¹f(s)g(s)\phi_n(s)\,d\mkern1mu s & \to 0 & & \mathrlap{f, g ∈ F. }
\end{align*}
where the functions $ f, g $ and $ \{\phi_n\} $ are taken to be in certain preassigned
\vskip 5ex
\noindent
conditions guaranteeing that
\begin{flalign*}
& & ∫_0¹f(s)\phi_n(s)\,d\mkern1mu s &\to 0 && \mathllap{f ∈ F. }
\end{flalign*}
\begin{flalign*}
& & ∫_0¹f(s)g(s)\phi_n(s)\,d\mkern1mu s &\to 0 & \mathllap{f, g ∈ F. }&
\end{flalign*}
where the functions $ f, g $ and $ \{\phi_n\} $ are taken to be in certain preassigned
\vskip 5ex
\noindent
conditions guaranteeing that
\begin{flalign*}
& & ∫_0¹f(s)\phi_n(s)\,d\mkern1mu s &\to 0 && \llap{\eqparbox{Q}{$ f ∈ F. $} }
\end{flalign*}
\begin{flalign*}
& & ∫_0¹f(s)g(s)\phi_n(s)\,d\mkern1mu s &\to 0 & \llap{\eqparbox{Q}{$ f, g ∈ F. $ }}&
\end{flalign*}
where the functions $ f, g $ and $ \{\phi_n\} $ are taken to be in certain preassigned
\end{document}

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