How do I prove the following?
If X is a Borel set, and , prove that is also a Borel set.
Thank you!
When you show that the generators (pi systems) are the same. So in this case the Borel sets are generated by the open sets. As , the sets of the form X+a are generated by U+a where U is open. If you know that the generators are the same, then you know that the sigma algebra they generate are the same as well.