NDLI: Radon—Nikodym Theorem in L ∞

Content Provider	Springer Nature Link
Author	Barron, E. N. Cardaliaguet, P. Jensen, R. R.
Abstract	We prove that for any given set function F which satisfies F(∪ A i ) =supi F(A i ) and F(A)=-∈fty if meas (A)=0 , there must exist a measurable function g so that F(A) = ess sup_ y ∈ A g(y) . Two proofs of this result are given. Then a Riesz representation theorem for ``linear'' operators on L ∈fty is proved and used to establish the existence of Green's function for first-order partial differential equations. In the special case u t +H(u,Du)=0 , Green's function is explicitly found, giving the extended Lax formula for such equations.
Starting Page	103
Ending Page	126
Page Count	24
File Format	PDF
ISSN	00954616
Journal	Applied Mathematics and Optimization
Volume Number	42
Issue Number	2
e-ISSN	14320606
Language	English
Publisher	Springer-Verlag
Publisher Date	2000-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization

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Radon—Nikodym Theorem in L ∞