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Weak convergence of linear forms in D[0, 1]

✍ Scribed by Peter Z Daffer; Robert L Taylor


Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
394 KB
Volume
13
Category
Article
ISSN
0047-259X

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Convergence of Weighted Sums and Laws of
✍ I. Schiopukratina; P. Daffer πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 426 KB

Convergence properties of weighted sums of functions in \(D([0,1] ; E)(E\) a Banach space) are investigated. We show that convergence in the Skorokhod \(J_{1}\)-topology of a sequence \(\left(x_{n}\right)\) in \(D([0,1] ; E)\) does not imply convergence of a sequence \(\left(\bar{x}_{n}\right)\) of