We study \YHd s of measures on orthomodular 
posets and lattices. 
We discuss the existence and uniqueness of 
decompositions into a convex combination of 
a completely additive measure and a measure 
which is either weakly purely finitely 
additive or filtering.
Then we are interested in the case of c-positive
orthomodular lattices which have ``enough" 
completely additive measures.
For this class of lattices we find several 
conditions equivalent to the requirement 
that the \YHd\ coincides with the \Rd. 
We present an example which shows that 
the uniqueness of the \YHd\ does not
imply the equality of the decompositions. 
As an application of the construction 
technique used therein, we answer a 
problem posed by G.~R\"uttimann: Can any 
completely additive Jordan measure
be expressed as a difference of completely 
additive positive measures? We prove that 
the completely additive Jordan measures 
on the c-positive orthomodular lattices allow 
for such an expression whereas for general
orthomodular lattices such a decomposition 
is generally not available.