Thus, we have the following definition : Let \ mu ^ * be an outer measure on a set X.
12.
The Lebesgue outer measure emerges as the greatest lower bound ( infimum ) of the lengths from among all possible such sets.
13.
Both versions concern the bisection of subsets of a common set, where has a Carath�odory outer measure and each has finite outer measure.
14.
Both versions concern the bisection of subsets of a common set, where has a Carath�odory outer measure and each has finite outer measure.
15.
Among the publications of Hausdorff in his time at Greifswald time the work " Dimension and outer measure " from 1919 is particularly outstanding.
16.
It can be seen that H ^ d ( S ) is an outer measure ( more precisely, it is a metric outer measure ).
17.
It can be seen that H ^ d ( S ) is an outer measure ( more precisely, it is a metric outer measure ).
18.
The first part of the definition states that the subset E of the real numbers is reduced to its outer measure by coverage by sets of intervals.
19.
The measure-category duality provides a measure analogue of Luzin sets sets of positive outer measure, every uncountable subset of which has positive outer measure.
20.
The measure-category duality provides a measure analogue of Luzin sets sets of positive outer measure, every uncountable subset of which has positive outer measure.
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