This article considers Savage's theorem in a configuration relaxing the technical axioms P6 and P7 that ensure a continuum nature on the set of states. With the only enrichment on fundamentals being the connectivity of the outcomes set, we show that a weakened version of the Independence property is sufficient to establish a utility function, a subjective probability, and an expected utility behavior. The proof does not require the existence of a pair event, an idea initiated by Ramsey (1931) and applied by Gul (1992).