  It is shown that quantum-induced (inflationary) brane Universe occurs in the
bulk 5d AdS black hole in accordance with AdS/CFT correspondence. Brane stress
tensor is induced by quantum effects of dual CFT and brane crosses the horizon
of AdS black hole. Quantum-corrected Hubble constant, Hawking temperature and
entropy are found on the brane (and at the horizon). The similarity between CFT
entropy at the horizon and FRW equations is extended on the quantum level. This
suggests the way to understand cosmological entropy bounds in quantum gravity.
