Group action and shift-compactness

Beyond Erdős-Kunen-Mauldin: Shift-compactness properties and singular sets

“…That is followed by its Haarmeasure version, Theorem 2H. The latter closely follows the argument in [MilO,Th. 1M].…”

“…In [MilO] the …rst and third authors studied extensions of the Kestelman-Borwein-Ditor theorem from the perspective of group action, on the one hand, and certain limitations (exempli…ed by 'singular'sets) of the in…nite combinatorics involved, on the other. The latter included 'wild' 2-placefunction actions in place of group actions [MilO,Th. 8], and examples of nonshift-compactness (existence, for a given closed nwd set A; of a monotonic null sequence with fd n g n2N so that for each x; x + d n = 2 A in…nitely often, and an example, under the Axiom of Choice, of a non-measurable A with x + (1=n) =…”

Beurling slow and regular variation

“…Here an early treatment is [1] followed by [2], but a full topological development dates from our recent papers (for which see [17,18], and for the particular role of group action [55,58]). Recall that a group action A : G × X → X requires two properties:…”

On Subadditive Functions Bounded Above on a “Large” Set

“…In the Euclidean context of [6] a shiftcompact set was earlier called subuniversal (following H. Kestelman [30]), and also nullshift-compact (in [11] in the special context of R). The underlying group action is studied in [37].…”