Open AccessRemarks on continuously distributed sequences
Author(s) -
Milan Paštéka
Publication year - 2021
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.13.1.89-97
Subject(s) - mathematics , sequence (biology) , simple (philosophy) , type (biology) , function (biology) , distribution (mathematics) , probability density function , measure (data warehouse) , pure mathematics , calculus (dental) , mathematical analysis , statistics , computer science , data mining , medicine , ecology , philosophy , genetics , dentistry , epistemology , evolutionary biology , biology
In the first part of the paper we define the notion of the density as certain type of finitely additive probability measure and the distribution function of sequences with respect to the density. Then we derive some simple criterions providing the continuity of the distribution function of given sequence. These criterions we apply to the van der Corput's sequences. The Weyl's type criterions of continuity of the distribution function are proven.