Let¤n denote the set of scenario trees with depth 1 and n scenarios. LetX = (0 · x1 < . . . < xn · 1) and let¤n(X) denote
the set of all scenario trees of depth 1 with the scenarios X = (0 · x1 < . . . < xn · 1). Let G be a probability distribution
defined on [0, 1] and H be a subset of measurable functions defined on [0, 1]. Let dH,X(G) = inf ˜G∈¤n(X) dH(G, ˜ G) and
dH(G) = inf ˜G∈¤n
dH(G, ˜ G), where dH(G, ˜ G) := suph∈H
¯¯¯
R h dG − R h d˜G
¯¯¯
. The main goal of the paper is to estimate
