2
\mathcal{P}^s_{\delta}(F) = sup \Bigg\{ \sum_{i}|B_i|^s : 
\{B_i\} \text{is a collection of disjoint balls of radii at most 
$\delta$ with centres in F} \Bigg\} 

This piece of text wont stay in the margins that I am writing in. I tried to put a line break, \, after the word "most" but it didnt do anything.

How can I rectify this?

3

As you've discovered, an ordinary equation environment won't let you insert line breaks. I suggest you load the amsmath package (if you're not already doing so) and use its align* environment to typeset the expression; insert & where you want the alignment points to be.

In the code below, I also make use of \smash[b]{...} to reduce the space between the two output lines. Incidentally, \Bigg would seem far too, well, big for the job at hand; I suggest using \Bigl and \Bigr to size the curly braces. Using \colon instead of : when in math mode will give you better spacing around the colon symbol. I also suggest using \textnormal rather than just \text, just in case the material occurs inside a theorem-like environment that italicizes text material.

enter image description here

\documentclass{article}
\usepackage{amsmath,amsthm}
\newtheorem{thm}{Theorem}
\begin{document}
\begin{align*}
\mathcal{P}^s_{\delta}(F) = \sup \smash[b]{\Bigl\{ \sum_{i}}|B_i|^s \colon 
&\textnormal{$\{B_i\}$ is a collection of disjoint balls}\\
&\textnormal{of radii at most $\delta$ with centres in $F$} \Bigr\} 
\end{align*}
\end{document}

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