On relation of measure-theoretic and special properties of $\mathbb Z^d$-actions

It is shown how using the $\kappa$-mixing property one can construct finite measure-preserving $\mathbb{Z}^{d}$-actions possessing different and even unusual properties. In the case of a “classical time” $\mathbb{Z}$ this approach was applied by Lemanczik and del Junco as an alternative to the so-called Rudolf's “counterexamples machine”, based on the notion of joining.