There is two ways to learn statistics. Statistical intuition vs. learning the core concepts. When probability is formulated using measure theory things really click together with the rest of the mathematics.
> That is math, not statistics.
Sometimes in the university level statistics department teaches applied statistics and you need to go mathematical department to learn mathematical statistics. What you think is 'real' statistics for you is matter of opinion, but non-applied statistics is pure abstract mathematics.
It's a mistake to think you're learning statistics when you're learning about measure theory, just like it's a mistake to think you're learning physics when you're learning about differential equations. The mathematical tools used in a subject are not the same as the subject itself.
There is two ways to learn statistics. Statistical intuition vs. learning the core concepts. When probability is formulated using measure theory things really click together with the rest of the mathematics.
> That is math, not statistics.
Sometimes in the university level statistics department teaches applied statistics and you need to go mathematical department to learn mathematical statistics. What you think is 'real' statistics for you is matter of opinion, but non-applied statistics is pure abstract mathematics.