𝔖 Bobbio Scriptorium
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Continuity and compactness of measures

✍ Scribed by J.K Brooks; R.V Chacon

Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
667 KB
Volume
37
Category
Article
ISSN
0001-8708

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It is proved that a weak\* compact subset A of scalar measures on a \_-algebra is weakly compact if and only if there exists a nonnegative scalar measure \* such that each measure in A is \*-continuous (such a measure \* is called a control measure for A). This result is then used to obtain a very g

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## Abstract Let Ξ© be an open subset of ℝ^__n__^ and let __p__ ∈ [1, __n__). We prove that the measure of non–compactness of the Sobolev embedding __W__^__k,p__^~0~(Ξ©) β†’ __L__^__p__\*^(Ξ©) is equal to its norm. This means that the entropy numbers of this embedding are constant and equal to the norm.