Measure-valued almost periodic functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

Measure-valued almost periodic functions

Authors:

L. I. Danilov

Affiliation:

(1) Institute of Physics and Engineering, Ural Division of the Russian Academy of Sciences, USSR

Abstract:

We consider Stepanov almost periodic functions μ ∈ $$mathcal{S}(mathbb{R},{text{ }}mathcal{M})$$

ranging in the metric space $$mathcal{M}$$

of Borel probability measures on a complete separable metric space $$mathcal{U}{text{ }}(mathcal{M}$$

is equipped with the Prokhorov metric). The main result is as follows: a function $$t to mu left[ { cdot ;t} right] in mathcal{M},{text{ }}t in mathbb{R}$$

, belongs to $$mathcal{S}(mathbb{R},{text{ }}mathcal{M})$$

if and only if for each bounded continuous function $mathcal{F} in C_b (mathcal{U},mathbb{R})$ , the function $int_u {mathcal{F}(x)mu [dx; cdot ]}$ is Stepanov almost periodic (of order 1) and

$Modmu = sumlimits_{mathcal{F} in C_b (mathcal{U},mathbb{R})} {Modint_u {mathcal{F}(x)mu [dx; cdot ]} .}$

Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 57–68, January, 1997. Translated by I. P. Zvyagin

Keywords:

almost periodic functions probability measures Stepanov almost periodicity

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏