We examine stochastic in math and got to expected values variances. I don't understand the definition of expected values. The following picture is in German.
It says: Is $X \in L^1(\Omega, \mathfrak{U}, P) $ an integrable random variable, then $$ E[X] = \int X d P $$
is the expectancy value of X.
I have no idea how to read this. How do you integrate over a random Variable X with P?
P is of course a probability measure.