Glossary of economics research
Results of search for B1 follow:
B1:
B1 denotes the Borel sigma-algebra of the real line. It
will contain every open interval by definition, which implies that it contains
every closed interval and every countable union of open, half-open, and closed
intervals.
What won't it contain? In practice, only obscure sets. Here's an example:
Define the equivalence class ~ on the real line such that x~y (read: x is in
the same equivalence class as y) if x-y is a rational number. Now consider
the set of all numbers in [0,1] such that none of them are in the same
equivalence class. How many members of that set are there? Well, it's not a
countable number. This set is not in B1.
Contexts: math; measure theory; real analysis
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