I am feeling a bit silly for asking this question, but I am having trouble understanding this notation for (iterated?) expectation wrt multiple random variables used in the book "Fast algorithms via Approximation theory" by Vishnoi and Sachdeva (there is no index of notation in the book)
What does the notation marked in yellow mean? Of course I understand what expectation is with respect to a single random variable, or the sum/product of a bunch of them, or indeed conditional expectation of a random variable with respect to another one.....But this $E$ with several variables underneath it, what kind of expectation is that?
It says iterated expectation in the sentence "this simple observation.." but I am getting stuck in understanding exactly what the iteration is....I underdstand intuitively what the theorem is trying to say, (write a monomial in the form of an appropriate expectation of a chebyshev polynomial) Or is this just the usual expectation taken over all values of $Y_i's$
