Games

A nice application to use all of our material on charges, measures and the sequence space ℓ1https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315166209/ca8d5048-0ada-4280-9f99-fd3bb3017999/content/ieq2875.tif"/> and dual spaces is something called game theory. A good theoretical discussion of this at a graduate level in analysis can be found in (Kunnai (12, Chapter 12) 1992). In Chapter 15, we gave you the background material on charges you will need. Now we can talk about simple games and connect the discussion to the sequence space c₀, its dual ℓ1https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315166209/ca8d5048-0ada-4280-9f99-fd3bb3017999/content/ieq2876.tif"/> and finally the sequence space ℓ∞https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315166209/ca8d5048-0ada-4280-9f99-fd3bb3017999/content/ieq2877.tif"/> and its dual ba(Ω,ℱhttps://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315166209/ca8d5048-0ada-4280-9f99-fd3bb3017999/content/ieq2878.tif"/>). Then we stop there as to do more is far beyond our brief here.