On exact atomless Milutin maps

Continuous linear extension of functions

“…Suppose β n = β for every n ∈ N. Since all the functions g n and g have the same domain and their graphs converge in the Hausdorff metric, we conclude that {g n } converges pointwise to g on dom g (see [9]). Then the sequence {g n • π 1 • ϕ} and the limit function g • π 1 • ϕ satisfy the hypothesis of Lebesgue's dominated convergence theorem and we obtain e(g n )(x n ) = e(g n )(x) → e(g)(x).…”

“…Proof. The fact that e(g) is a continuous, bounded function on X follows from continuity and boundedness of the function g • π 1 • ϕ on m −1 (X × {dom g}) and continuity of the measures. Indeed, for a sequence {x i } from X converging to some…”

Probability measures and Milyutin maps between metric spaces

“…Moreover, λ i ε for at least one i. For each i k and n 1 choose a neighborhood V i ⊂ K of x i and n different points x i (1) , . .…”

“…Hence, if g is a choice map associated with f , E-mail address: veskov@nipissingu.ca. 1 The author was partially supported by NSERC Grant 261914-08. Our first principal result concerns the question whenP (f ) is a soft map.…”

“…It also provides a partial answer of the question [1] whether any open surjection f of complete spaces is an exact atomless Milyutin map provided all fibers of f are perfect Polish spaces. …”