Definition talk:Restricted Measure

User:Usagiop, I just realised that $\Sigma'$ must have the same underlying set in this definition, my mistake. Should we create a subpage of this page (or a slightly different page) talking about restrictions of a measure to a trace $\sigma$-algebra of a measurable set. It's just a function restriction at the end of the day, (and there is nothing weird going on if the trace-$\sigma$-algebra is over a measurable set, since it's nothing but the measurable subsets of that set) basically all properties will be preserved in a natural way. Something like "Restriction of Measure to Trace $\sigma$-algebra". I am not sure if any source will have bothered to introduce this specifically, so I think we are good foregoing a source for now. Caliburn (talk) 18:16, 16 June 2022 (UTC)