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November 15th, 2015, 06:02 AM   #1
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help in real analysis

What is the difference between measure and outer measure ?

Last edited by greg1313; November 15th, 2015 at 07:45 PM.
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November 15th, 2015, 08:12 PM   #2
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You need to fully understand the meaning of measurable sets. All sets have outer measure, but only measurable sets have measure.
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November 18th, 2015, 06:00 AM   #3
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It's confusing because measure, outer measure, and inner measure all use the same algorithm. We can apply that same algorithm to any set.

When we have a "nice" set, then outer measure and inner measure agree, and we say the set is measurable, and we drop "outer" and "inner" and simply speak of the set's measure.

But if we have an "not nice" (i.e., non-measurable set) then inner and outer measure don't agree so the measure of the set is undefined.
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