Compactness of The Borel Probability Measure

• 발행기관: 호서대학교 기초과학연구소
• 저자명: Gui Seok Kim Kyung Bok Lee
• 간행물 정보: 『기초과학연구 논문집』제21권 제1호, 1~7쪽, 전체 7쪽
• 주제분류: 공학 > 공학일반
• 파일형태: PDF
• 발행일자: 2013.12.30

영문 초록

Given a compact metric space (X,d), we denote by M(X) the set of all Borel probability measures in X . To show that M(X) is metrizable, we will define metric p :/M (X) X M (X) →R0+ by p(μ,v) = ∑∞n=1 2n/1 I ∫x φ ndv I. Finally, we prove that If is a compact metric space, then a metric space (M (X),p) is compact.

목차

1. Introduction and Preliminaries

2. Compactness of the Borel Probability Measure

키워드

Compactness Borel Probability Measure