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psie
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- TL;DR Summary
- I am reading Folland's text on real analysis. He defines the Borel
-algebra on the extended reals and says this coincides with the usual definition of the Borel -algebra being generated by open sets. I don't see how they coincide.
On page 45 in Folland's text on real analysis, he writes that we define Borel sets in by . Then he remarks that this coincides with the usual definition of the Borel -algebra if we make into a metric space with metric .
I don't see how the two coincide and would be grateful if someone could explain in more detail. I see how is a metric on , where e.g. should evaluate to , but I don't see how coincides with the usual definition of being generated by the open sets in . In other words, how to show
I don't see how the two coincide and would be grateful if someone could explain in more detail. I see how