Let (X, 7, +) be a finite, nonatomic, measure space. Let G=span[g 1 , g 2 , ..., g n ] L 1 , and let the support of G be X, a.e. For f # L , put . This paper characterizes when the functions, s, in Liapunov's theorem can further be restricted to being the signs of continuous functions. That is, sup
Extremal Faces of the Range of a Vector Measure and a Theorem of Lyapunov
โ Scribed by Stefano Bianchini
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 140 KB
- Volume
- 231
- Category
- Article
- ISSN
- 0022-247X
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๐ SIMILAR VOLUMES
Let R R be a ring of subsets of a nonempty set โ and โบ R R the Banach space of uniform limits of sequences of R R-simple functions in โ. Let X be a quasicom-ลฝ . plete locally convex Hausdorff space briefly, lcHs . Given a bounded X-valued ลฝ . vector measure m on R R, the concepts of m-integrability
let m โ E be a finitely additive measure with finite semivariation, defined on a ฮด-ring of subsets of a given set S. A theory of integration of vector-valued functions f S โ E, applicable to the stochastic integration in Banach spaces, is developed in [6, Sect. 5]. Many times a measure m is defined