Exchangeable lower previsions

We extend de Finetti’s [Ann. Inst. H. Poincar'{e} 7 (1937) 1–68] notion of exchangeability to finite and countable sequences of variables, when a subject’s beliefs about them are modelled using coherent lower previsions rather than (linear) previsions. We derive representation theorems in both the finite and countable cases, in terms of sampling without and with replacement, respectively.