The question is pretty straightforward.
I'm an actuary with a bachelor and a master degree in actuarial science. I have already worked in the insurance industry, I have programming experience and some data science/machine learning background thanks to Kaggle, MOOCs and similar stuff.
As an actuary, I have had a lot of stats classes but I'm not sure if what I have studied is enough for a PhD in Statistics or if I lack a lot of things (i.e. I have never studied measure theory). What do you think about it? Is it possible to enter in a good statistics program in Europe?
My research would be in ML and similar things applied to actuarial. I also want to enter in a good university because I want to become a professor.