Abstract
AbstractWe prove that the lower density operator associated with intensity points on the real line has Borel values. We also prove that the simple density operator and the complete density operator have Borel values.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
Reference16 articles.
1. Andretta, A., Camerlo, R.: The descriptive set theory of the Lebesgue density theorem. Adv. Math. 244, 1–42 (2013)
2. Balcerzak, M., Hejduk, J., Wachowicz, A.: Baire category lower density operators with Borel values. Results Math. 78, 2 (2023)
3. Ciesielski, K., Larson, L., Ostaszewski, K.: $${\cal{I} }$$-density continuous functions. Mem. Am. Math. Soc. 107(515), 133 (1994)
4. Hejduk, J., Loranty, A.: On abstract and almost-abstract density topologies. Acta Math. Hung. 155, 228–240 (2018)
5. Hsu, P.L., Robbins, H.: Complete convergence and the law of large numbers. Proc. Nat. Acad. Sci. USA 33, 25–31 (1947)