  We investigate the problem of common randomness (CR) generation in the basic
two-party communication setting in which a sender and a receiver aim to agree
on a common random variable with high probability. The terminals observe
independent and identically distributed (i.i.d.) samples of sources with an
arbitrary distribution defined on a Polish alphabet and are allowed to
communicate as little as possible over a noisy, memoryless channel. We
establish single-letter upper and lower bounds on the CR capacity for the
specified model. The derived bounds hold with equality except for at most
countably many points where discontinuity issues might arise.
