  Del Junco--Lema\'nczyk showed that a generic measure preserving
transformation satisfies a certain orthogonality conditions. More precisely,
there is a dense $G_\delta$ subset of measure preserving transformations such
that for every $T\in G$ and $k(1), k(2), \dots, k(l)\in \mathbb{Z}^+$, $k'(1),
k'(2), \dots, k'(l')\in \mathbb{Z}^+$, the convolutions \[ \sigma_{T^{k(1)}}
\ast\cdots\ast \sigma_{T^{k(l)}} \ \text{and} \ \sigma_{T^{k'(1)}} \ast\cdots
\ast\sigma_{T^{k'(l')}} \] are mutually singular, provided that $(k(1), k(2),
\dots, k(l))$ is not a rearrangement of $(k'(1), k'(2), \dots, k'(l'))$. We
will introduce an analogous orthogonality conditions for continuous unitary
representations of $L^0(\mu,\mathbb{T})$ which we denote by DL--condition. We
connect the DL--condition with a result of Solecki which states that every
continuous unitary representations of $L^0(\mu,\mathbb{T})$ is a direct sum of
action by pointwise multiplication on measure spaces
$(X^{|\kappa|},\lambda_\kappa)$ where $\kappa$ is an increasing finite sequence
of non-zero integers. In particular, we show that the "probabilistic"
DL-condition translates to "deterministic" orthogonality conditions on the
measures $\lambda_\kappa$.
