As far as I understand if we have channel which has random capacity for each discrete time moment (for example Rayleigh fading ), then

**the capacity is just average capacity.**

I am trying to understand it.

It seems the following simpliefied situation should be understand first: consider the two channels assume we know that capacity of one of them is c1 , capacity of another is c2, but we do not know what channel has c1, what channel has c2. Nevetheless it seems that capacity is c1+c2, the same as as if we know what channel has c1, what channel has c2...

For example if we consider AWGN channels - can one suggest some simple proof of this ?

(Similar to proof of capacity for AWGN with balls filling )