=+18. Let f(t) be a nonnegative function on (0, ∞) with limt→0 f(t) = 0.

If f(t) is subadditive in the sense that f(s + t) ≤ f(s) + f(t) for all positive s and t, then show that lim t↓0 f(t)

t = sup t>0 f(t)

t = q.

(Hint: Demonstrate that p ≤ lim inf t↓0 f(t)

t ≤ lim sup t↓0 f(t)

t for all p ∈ [0, q).)