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In this paper, we extend the notions of states and measures presented in\cite{DvPu} to the case of pseudo-BCK algebras and study similar properties. Weprove that, under some conditions, the notion of a state in the sense of\cite{DvPu} coincides with the Bosbach state, and we extend to the case ofpseudo-BCK algebras some results proved by J. K\"uhr only for pseudo-BCKsemilattices. We characterize extremal states, and show that the quotientpseudo-BCK algebra over the kernel of a measure can be embedded into thenegative cone of an archimedean $\ell$-group. Additionally, we introduce aBorel state and using results by J. K\"uhr and D. Mundici from \cite{Kumu}, weprove a relationship between de Finetti maps, Bosbach states and Borel states.

Measures, states and de Finetti maps on pseudo-BCK algebras