I've recently started to study measure theory and in this respect am reading up on sigma algebras. In this context I saw that sometimes collections are denoted as calligraphic letters (also called algebras) containing other sets. However, for $\mathcal{A} = \{\emptyset, \Omega\}$ a text I read has "The set $\mathcal{A} = \{\emptyset, \Omega\}$ for any set $\Omega$". This confused me aboout whether the term 'collection' has any specific restrictions to be used, i. e. whether the sets contained in a collection have to configured in a certain way; my question therefore:
Is the set $\mathcal{A} = \{\emptyset, \Omega\}$ a collection?
Best Answer
A collection is a set in this context.
The set $\mathcal A$ is a set of set, so $\mathcal A$ is definitely a set. Because it is a set of sets, it is sometimes informally called a collection or a collection of sets
(sometimes collection refers to something slightly different, see the comment of Gae. S., but not in this context.)