If f; g F(X) are increasing, then f + g is increasing f is

If f; g ∊ F(X) are increasing, then
• f + g is increasing
• αf is increasing for every α ≥ 0
Therefore the set of all increasing functionals on a set X is a cone in F(X).
Moreover, if f is strictly increasing, then
• f + g is strictly increasing
• αf is strictly increasing for every α > 0