We say a generic element of a Polish space satisfies a property if the property holds for every element in a countable intersection of open and dense subsets. Del Junco and Lemanczyk showed certain orthogonality conditions for a generic measure preserving transformation on the maximal spectral type of powers of the transformation . We introduce an analogous condition (DL-condition) for unitary representations of the group of measurable functions from the real numbers with the Lebesgue measure to the unit circle. Solecki showed that one can identify each such unitary representation with a sequence of measures. We will show that the DL-condition is equivalent to some orthogonality conditions on this sequence of measures. Also, we will show that generic measurable functions are somewhat independent, in particular, the range of two generic measurable functions are almost disjoint.
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