# Convergence theorems for monotone measures

Jun Li, Radko Mesiar, E. Pap, Erich Peter Klement

Research output: Contribution to journalArticle

20 Citations (Scopus)

### Abstract

In classical measure theory there are a number of convergence theorems, such as the Egorov, the Riesz and the Lusin theorem, among others. We consider monotone measures (i.e., monotone set functions vanishing in the empty set and defined on a measurable space) and discuss, how and to which extent classical convergence theorems can be carried over to this more general case.

Original language English 103-127 25 Fuzzy Sets and Systems 281 https://doi.org/10.1016/j.fss.2015.05.017 Published - Dec 15 2015

### Fingerprint

Convergence Theorem
Monotone
Measurable space
Measure Theory
Null set or empty set
Theorem

### Keywords

• Convergence theorems
• Egorov theorem
• Lusin theorem
• Monotone measure
• Monotone set function
• Riesz theorem

### ASJC Scopus subject areas

• Artificial Intelligence
• Logic

### Cite this

Convergence theorems for monotone measures. / Li, Jun; Mesiar, Radko; Pap, E.; Klement, Erich Peter.

In: Fuzzy Sets and Systems, Vol. 281, 15.12.2015, p. 103-127.

Research output: Contribution to journalArticle

Li, Jun ; Mesiar, Radko ; Pap, E. ; Klement, Erich Peter. / Convergence theorems for monotone measures. In: Fuzzy Sets and Systems. 2015 ; Vol. 281. pp. 103-127.
@article{8ad00994a5a6424ca1d8075b292bf0b9,
title = "Convergence theorems for monotone measures",
abstract = "In classical measure theory there are a number of convergence theorems, such as the Egorov, the Riesz and the Lusin theorem, among others. We consider monotone measures (i.e., monotone set functions vanishing in the empty set and defined on a measurable space) and discuss, how and to which extent classical convergence theorems can be carried over to this more general case.",
keywords = "Convergence theorems, Egorov theorem, Lusin theorem, Monotone measure, Monotone set function, Riesz theorem",
author = "Jun Li and Radko Mesiar and E. Pap and Klement, {Erich Peter}",
year = "2015",
month = "12",
day = "15",
doi = "10.1016/j.fss.2015.05.017",
language = "English",
volume = "281",
pages = "103--127",
journal = "Fuzzy Sets and Systems",
issn = "0165-0114",
publisher = "Elsevier",

}

TY - JOUR

T1 - Convergence theorems for monotone measures

AU - Li, Jun

AU - Mesiar, Radko

AU - Pap, E.

AU - Klement, Erich Peter

PY - 2015/12/15

Y1 - 2015/12/15

N2 - In classical measure theory there are a number of convergence theorems, such as the Egorov, the Riesz and the Lusin theorem, among others. We consider monotone measures (i.e., monotone set functions vanishing in the empty set and defined on a measurable space) and discuss, how and to which extent classical convergence theorems can be carried over to this more general case.

AB - In classical measure theory there are a number of convergence theorems, such as the Egorov, the Riesz and the Lusin theorem, among others. We consider monotone measures (i.e., monotone set functions vanishing in the empty set and defined on a measurable space) and discuss, how and to which extent classical convergence theorems can be carried over to this more general case.

KW - Convergence theorems

KW - Egorov theorem

KW - Lusin theorem

KW - Monotone measure

KW - Monotone set function

KW - Riesz theorem

UR - http://www.scopus.com/inward/record.url?scp=84945455372&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84945455372&partnerID=8YFLogxK

U2 - 10.1016/j.fss.2015.05.017

DO - 10.1016/j.fss.2015.05.017

M3 - Article

AN - SCOPUS:84945455372

VL - 281

SP - 103

EP - 127

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

SN - 0165-0114

ER -