Vector‐Valued Choquet Theory and Transference of Boundary Measures | Zendy

Batty C. J. K. | Zendy

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Vector‐Valued Choquet Theory and Transference of Boundary Measures

Author(s) -

Batty C. J. K.

Publication year - 1990

Publication title -

proceedings of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.899

H-Index - 65

eISSN - 1460-244X

pISSN - 0024-6115

DOI - 10.1112/plms/s3-60.3.530

Subject(s) - mathematics , uniqueness , banach space , hausdorff space , pure mathematics , bounded function , choquet theory , boundary (topology) , space (punctuation) , hausdorff measure , measure (data warehouse) , locally compact space , mathematical analysis , discrete mathematics , hausdorff dimension , geometry , subderivative , convex optimization , regular polygon , linguistics , philosophy , database , computer science

Let X be a compact Hausdorff space, E be a real Banach space and A be a linear space of continuous functions of X into E , separating points and containing constants. Let M ( X , E * ) be the space of regular E * ‐valued measures on X of bounded variation. For E = C , Roth has shown that M ( X , C ) may be ordered in such a way that the maximal measures are precisely the boundary measures for A . This ordering is extended to a general E , and it is shown that the appropriate existence and uniqueness theorems can be deduced from real Choquet theory by transferring E * ‐valued measures on X into positive measures on X ×E 1 ∗ .

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