Suppose that $([0,3], \sigma([0,3]))$ and $([0,\infty], \mathcal{A})$, with $\mathcal{A} =\{\emptyset, [0,\infty]\}$. Using $f: [0,3] \to [0, \infty]$ such that $f(x)=x^2$, then is $f$ measurable?
I am having trouble identifying if the function $f$ is measurable. However, my theory is that it is not measurable, but dont know how to prove it or why it is true (that it is not measurable)