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Continuous selections on metric continuum
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admits a selection analytic set assume barycentric Blackwell space Borel function Borel measurable Borel set Borel subset bounded variation choice theorem classical solution closed set compact metric space complete separable metric completes the proof contains continuous function continuous selection continuum convex set convex subsets countable set cut point defined Definition extreme points f is continuous ff-field finite fixed point function f G is open hence induction integer Kuratowski Lebesgue measurable lemma Let f limsup Lusin Math measurable function n-simplex neighbourhood non-cut points numbers open set order isomorphism paracompact paracompact space Player Polish space proof of theorem proposition prove the following Remark satisfies selection theorem due selector separable metric space sequence set-valued function set-valued measure stochastic game Suppose theorem 5.1 topological space uniformising set uniformly valued function XePg