A category analogue of the density topology

On Directional I 1- Density Points

“…fc is Sk -measurable if and only if A £ SkFor A 6 «Si, we shall denote by <j>{A) the set of all Ij-density points of A [6]. It is known [6] that the mapping <j) : Si -• is a lower density operator.…”

On Riemann-Type Definition for the Wide Denjoy Integral

“…Among others, the dyadic local system D d [1], the proximal density local system D pro [17], and the s -density local system [15]. All of them are bilateral and (except D pro ) satisfy IC.…”

Weak convergence with respect to category

“…It is worth mentioning that the weak convergence in measure may be useful in defining the density of a set at a point (compare [5], Prop. 3 and [3]). The definition below is constructed in the spirit of [1], p. 149, 9.13 or [2], Cor.…”