  Inhomogeneous multinomial measures on the mixed symbolic spaces and the real
line are given. By counting the zeros of the corresponding generalized
Dirichlet polynomials, one obtains a probability measure whose Olsen's
functions $b$ and $B$ are analytic and their graphs differ except at two points
where they are tangent. Also, interpretations of the Legendre transform of $b$
and $B$ are given in terms of dimensions.
