We study the relationship between the σ-ideal generated by closed measure zero sets and the ideals of null and meager sets. We show that the additivity of the ideal of closed measure zero sets is not bigger than covering for category. As a consequence we get that the additivity of the ideal of closed measure zero sets is equal to the additivity of the ideal of meager sets.

In this paper, we study properties of the stationary harmonic measure which are unique to case. We prove that any subset with an appropriate sub-linear horizontal growth has a non-zero measure. On other hand, show at least linear will have 0 every point. This result is fundamental future DLA. As application possible aggregation process rates proportional non zero all times.