Thank you for the paper. Nevertheless I think that for the pure isotropic sky map it should be possible to derive an analytical expression, if the N events have instead of all weights ω_i=1 (for this case the above expression is true) different weights ω_i for each event i.
If e.g. N/4 events...
My general question is:
What is the angular power spectrum C_{l,N,ω} of N weighted (weight ω_i for event i) events from a full sky map with distribution C_l?
I'm interested in:
Mean of C_{l,N,ω}: <C_{l,N,ω}>
Variance of C_{l,N,ω}: Var(C_{l,N,ω})
The question is important, since we observe in...