For , if g F () is increasing, then the correspondence G() = {x:

For Θ ∊ ℜ, if g ∊ F (Θ) is increasing, then the correspondence G(θ) = {x: 0 ≤ x ≤ g(θ)}
is increasing
The significance of this definition of monotonicity for correspondences is that every monotone correspondence has a monotone selection. This and other useful properties of monotone correspondences are detailed in the following exercises.