Outer Measure and Topology
Suppose (X, d) is a metric space and φ an outer measure on X. If φ has the property that
whenever
then φ is called a metric outer measure.
Theorem. If φ is a metric outer measure on X, then every Borel subset of X is φ-measurable. (The Borel sets of X are the elements of the smallest σ-algebra generated by the open sets.)
Read more about this topic: Outer Measure
Famous quotes containing the words outer and/or measure:
“After one look at this planet any visitor from outer space would say “I WANT TO SEE THE MANAGER.””
—William Burroughs (b. 1914)
“From whatever you wish to know and measure you must take your leave, at least for a time. Only when you have left the town can you see how high its towers rise above the houses.”
—Friedrich Nietzsche (1844–1900)