  Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra equipped with a
normal faithful state $\varphi$, and let $\Phi$ be a growth function. We
consider Haagerup noncommutative Orlicz spaces $L^\Phi(\M,\varphi)$ associated
with $\M$ and $\varphi$, which are analogues of Haagerup $L^p$-spaces. We show
that $L^\Phi(\M,\varphi)$ is independent of $\varphi$ up to isometric
isomorphism. We prove the Haagerup's reduction theorem and the duality theorem
for this spaces. As application of these results, we extend some noncommutative
martingale inequalities in the tracial case to the Haagerup noncommutative
Orlicz space case.
