Is Ω(f+g) = Ω(min(f,g))?
Assuming $f,g &gt; 0$, we have
$$\max(f(x),g(x)) &lt; f(x) + g(x) \leq 2\max(f(x),g(x)).$$
Therefore $\Theta(f(x) + g(x)) = \Theta(\max(f(x),g(x)))$, in the sense that both sets of functions are equal.

Still assuming that $f,g &gt; 0$, it is also true that $\Omega(f(x)+g(x)) = \Omega(\min(f(x),g(x)))$, in the sense that if $h(x) \in \Omega(f(x)+g(x))$ then also $h(x) \in \Omega(\min(f(x),g(x))$. The stronger bound $\Omega(f(x)+g(x)) = \Omega(\max(f(x),g(x)))$ also holds.

I have mentioned two interpretations of equality. In fact the second one (which really corresponds to $\subseteq$ in this case) is actually the standard one – equality is not symmetric! However, in the case of big $\Theta$ both notions fortunately coincide.