Modify the estimate in Theorem 10.4 in such a way that it is weakly and strongly universally consistent. Hint: Choose An ∈ R+ such that An tends “not too quickly” to infinity. Define Fn as the set of...

Modify the estimate in Theorem 10.4 in such a way that it is weakly and strongly universally consistent. Hint: Choose An ∈ R+ such that An tends “not too quickly” to infinity. Define Fn as the set of all piecewise polynomials of degree M (or less) with respect to an equidistant partition of [−An, An] consisting of Kn intervals, and extend these functions on the whole R by setting them to zero outside [−An, An].