Let be some measurable domain and f : E → R a measurable map. Let...
Let be some measurable domain and a measurable map. Let be a Borel set. Show that is measurable.
I'm advised to define . Now consists of sets whose preimage is measurable, and since is continuous these sets are open. This collection seems to form a -algebra on , but I'm confused about the construction here as it seems that is the smallest -algebra containing open sets, but that would mean that it's equal to ?