 For a detailed exposition of imprecise probability theory, see Levi (1980), van Fraassen (1990), Walley (1991) and Kyburg and Teng (2001). For excellent introductions see Mahtani (2019), as well as the entry on  imprecise probability  and its  technical  and  historical  appendices. See Weichselberger (2000) for an approach that avoids sets of probability functions by assigning credal intervals \([a,b]\subseteq[0,1]\) directly to propositions. For a sophisticated recent view on which the contents of beliefs are sets of probability functions, see Moss (2018). 