Abstract
It is proved that the Stanley conjecture holds for monomial ideals of mixed products, i.e., if $I$ is an ideal of mixed products in a polynomial ring $S$ over a field, then ${\rm sdepth}_S(I) \geq {\rm depth}_S(I)$ and ${\rm sdepth}_S(S/I) \geq {\rm depth}_S(S/I)$.
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