  We generalize the uniform common randomness capacity formula, initially
established by Ahslwede and Csisz\'ar for a two-source model for common
randomness generation from independent and identically distributed (i.i.d.)
discrete sources with unidirectional communication over rate-limited discrete
noiseless channels to the case when the one-way communication is over arbitrary
single-user channels. In our proof, we will make use of the transmission
capacity formula established by Verd\'u and Han for arbitrary point-to-point
channels.
