 for any non-negative integer "n", the Euclidean space ℝ"n" when considered as the space C({1, ..., "n"}, ℝ) where "S" = {1, ..., "n"} is given the discrete topology.The space formula_3 of all measurable almost-everywhere bounded real-valued maps on ℝ, where the preorder is defined for all "f", "g" ∈ formula_3 by "f" ≤ "g" if and only if "f"("s") ≤ "g"("s") almost everywhere.An order interval in a preordered vector space is set of the form 
From axioms 1 and 2 above it follows that "x","y" ∈ ["a","b"] and 0 < λ < 1 implies λ"x" + (1 − "λ")"y" in ["a","b"]; 
thus these order intervals are convex.