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Questions about asymptotic notations and analysis
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If $f(n)=\omega(h(n))$ and $g(n)=o(h(n))$ then is $f(n)=\Theta(g(n))$?
My question is exactly what the title says. If I have that $f(n)=\omega(h(n))$ and $g(n)=o(h(n))$ hold, then does $f(n)=\Theta(g(n))$ hold as well? My intuition says that the second part is false, but …