# Groups of homeomorphisms of the line. Criteria for the existence of invariant and projectively invariant measures in terms of the commutator subgroup

## Abstract

Existence criteria for invariant and projectively invariant measures are obtained for a group G of homeomorphisms of the line. These criteria are formulated in terms of the commutator subgroup [G,G]. For the special (but very important) case of groups of homeomorphisms of the line containing a freely acting element we obtain a criterion for the existence of a projectively invariant measure in the form of the absence of a special subgroup with two generators in which one of the generating elements is a freely acting element. Bibliography: 20 titles.

- Authors:

- Central Economics and Mathematics Institute, RAS, Moscow (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22364156

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 12; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; CALCULATION METHODS; COMMUTATORS; GROUP THEORY; INVARIANCE PRINCIPLES; MATHEMATICAL SOLUTIONS

### Citation Formats

```
Beklaryan, L A.
```*Groups of homeomorphisms of the line. Criteria for the existence of invariant and projectively invariant measures in terms of the commutator subgroup*. United States: N. p., 2014.
Web. doi:10.1070/SM2014V205N12ABEH004437.

```
Beklaryan, L A.
```*Groups of homeomorphisms of the line. Criteria for the existence of invariant and projectively invariant measures in terms of the commutator subgroup*. United States. doi:10.1070/SM2014V205N12ABEH004437.

```
Beklaryan, L A. Wed .
"Groups of homeomorphisms of the line. Criteria for the existence of invariant and projectively invariant measures in terms of the commutator subgroup". United States.
doi:10.1070/SM2014V205N12ABEH004437.
```

```
@article{osti_22364156,
```

title = {Groups of homeomorphisms of the line. Criteria for the existence of invariant and projectively invariant measures in terms of the commutator subgroup},

author = {Beklaryan, L A},

abstractNote = {Existence criteria for invariant and projectively invariant measures are obtained for a group G of homeomorphisms of the line. These criteria are formulated in terms of the commutator subgroup [G,G]. For the special (but very important) case of groups of homeomorphisms of the line containing a freely acting element we obtain a criterion for the existence of a projectively invariant measure in the form of the absence of a special subgroup with two generators in which one of the generating elements is a freely acting element. Bibliography: 20 titles.},

doi = {10.1070/SM2014V205N12ABEH004437},

journal = {Sbornik. Mathematics},

number = 12,

volume = 205,

place = {United States},

year = {Wed Dec 31 00:00:00 EST 2014},

month = {Wed Dec 31 00:00:00 EST 2014}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.