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Define: Exterior Measure
If is any subset of , the exterior measure of where is any countable covering of E.

Define: Measurable set
A set of is measurable if for all positive there exists and open set such that .

What are the 6 properties of Measure ?
 1) Every open set is measurable.
 2) If the set has exterior measure zero it is measurable.
 3) The countable union of measurable sets is measurable.
 4) Closed sets are measurable.
 5) The complement of a measurable set is measurable.
 6) The countable intersection of measurable sets is measurable.

Why is exterior measure insufficient. property does measure have the exterior measure not?
Measure of the union is equal to the sum of the measures when the sets are disjoint. This is not true for exterior measure.

Define: Measurable Function.
a function defined on a set E, is measurable if for all the set is measurable.


