Information content is classically measured by entropy measures in probability theory, that can be interpreted as a measure of internal inconsistency of a probability distribution. While extensions of Shannon entropy have been proposed for quantifying information content of a belief function, other trends have been followed which rather focus on the notion of consistency between sets. Relying on previous general entropy measures of probability, we propose in this paper to establish some links between the different measures of internal inconsistency of a belief functions. We propose a general formulation which encompasses inconsistency measures derived from Shannon entropy as well as those derived from the N-consistency family of measures.