Before revision:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega ] \left( \frac{n^{1/c}{2^c}} space.
After revision:  Combined with the 3/2-approximation for insertion-only streams by Cabello and Perez-Lanterno ] \left( \frac{n^{1/c}{2^c}} space.