big o - Prove max(O(f(n)), O(g(n)))=O(max(f(n), g(n)) -

prove max(o(f(n)), o(g(n)))=o(max(f(n), g(n)) 

it make sense, far don't have idea how prove it.

any input appreciated.

f(n) <= max(f(n), g(n)) g(n) <= max(f(n), g(n))  max(o(f(n)), o(g(n))) <= o(max(f(n), g(n)), max(f(n), g(n))) = o(max(f(n), g(n))) 

note in-equalities used not strict.