Show that a TP-coalitional game (N; w) is convex if and only if w(T {i}) - w

Question:

Show that a TP-coalitional game (N; w) is convex if and only if
w(T ∪{i}) - w (T) ≥ w (S ∪ {i}) - w(S)
for every i ∊ N and for every S ⊂ T ⊂ N / {i}
The marginal contribution of every player increases with the size of the coalition to which the player is joined.