On The Integral Representation of Strictly Continuous Set-Valued Maps

Lakmon, Anaté K.; Siggini, Kenny K.

Research Article

On The Integral Representation of Strictly Continuous Set-Valued Maps

Anaté K. Lakmon¹*
Kenny K. Siggini

University of Lome (TOGO)

* Corresponding author

Abstract

Let T be a completely regular topological space and C(T) be the space of bounded, continuous real-valued functions on T. C(T) is endowed with the strict topology (the topology generated by seminorms determined by continuous functions vanishing at in_nity). R. Giles ([13], p. 472, Theorem 4.6) proved in 1971 that the dual of C(T) can be identi_ed with the space of regular Borel measures on T. We prove this result for positive, additive set-valued maps with values in the space of convex weakly compact non-empty subsets of a Banach space and we deduce from this result the theorem of R. Giles ([13], theorem 4.6, p.473).

How to Cite

A. K. Lakmon, K. K. Siggini, On The Integral Representation of Strictly Continuous Set-Valued Maps, Int. J. Anal. Appl. 9 (2015), 114–120.

BibTeX

@article{Lakmon2015,
  author  = {Lakmon, Anaté K. and Siggini, Kenny K.},
  title   = {On The Integral Representation of Strictly Continuous Set-Valued Maps},
  journal = {Int. J. Anal. Appl.},
  volume  = {9},
  year    = {2015},
  pages   = {114--120},
  doi     = {}
}

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