Year: 2017
Type: preprint
Abstract: We define a generalization of the arithmetic mean to bounded transfinite sequences of real numbers. We show that every probability space admits a transfinite sequences of points such that the measure of each measurable subset is equal to the frequency with which the sequence is in this subset. We include an argument suggested by Woodin that the club filter on $ω_1$ does not admit such a sequence of order type $ω_1$.
Source: arXiv (Cornell University)
Author: Kornell, Andre
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2746940318