Does the master theorem apply for ≤ inequalities?

Question

Does the master theorem specifically apply when the recurrence contains ≤, ie. $T(n) ≤ 4T(n/2) + n$ ?

I cannot seem to find a definition containing inequalities.

Answer 1

Well, the Master Theorem lets you find the Big-O upper bound of a function $T(n)$ as $n \to \infty$. And it's easy to see that if $T(n) = aT(n/b) + f(n)$ implies $T(n) = \Theta(g(n))$, then $T(n) \leq aT(n/b) + f(n)$ would imply $T(n) = O(g(n))$ by induction on $n$.