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A-ergodicity of probability measures on locally compact groups
Let G be a locally compact group with the left Haar measure m G and let A = a n , k n , k = 0 ∞ be a strongly regular matrix. We show that if μ is a power bounded measure on G , then there exists an idempotent measure θ μ such that w*- lim n → ∞ ∑ k = 0 ∞ a n , k μ k = θ μ . If μ is a probability me...
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| Published in: | Archiv der Mathematik 2024, Vol.122 (1), p.47-57 |
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| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c270t-563e07cc7d326b2197fedcbb236e68301019df0a63ede1cdd42f6086576b639e3 |
| container_end_page | 57 |
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| container_start_page | 47 |
| container_title | Archiv der Mathematik |
| container_volume | 122 |
| creator | Mustafayev, Heybetkulu |
| description | Let
G
be a locally compact group with the left Haar measure
m
G
and let
A
=
a
n
,
k
n
,
k
=
0
∞
be a strongly regular matrix. We show that if
μ
is a power bounded measure on
G
, then there exists an idempotent measure
θ
μ
such that
w*-
lim
n
→
∞
∑
k
=
0
∞
a
n
,
k
μ
k
=
θ
μ
.
If
μ
is a probability measure on a compact group
G
, then
w*-
lim
n
→
∞
∑
k
=
0
∞
a
n
,
k
μ
k
=
m
¯
H
,
where
H
is the closed subgroup of
G
generated by
supp
μ
and
m
¯
H
is the measure on
G
defined by
m
¯
H
E
:
=
m
H
E
∩
H
for every Borel subset
E
of
G
. |
| doi_str_mv | 10.1007/s00013-023-01938-y |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2912680002</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2912680002</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-563e07cc7d326b2197fedcbb236e68301019df0a63ede1cdd42f6086576b639e3</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWKt_wNOC5-gkaZPsRShFq1DwouAtZJNs2bJt1mT3sP_eqSt48zAMwzzvfLyE3DK4ZwDqIQMAExQ4BiuFpuMZmbEFB6qxOicz7Auqdfl5Sa5y3iPNtSpn5HFFQ9pF37imH4tYF12Kla2a9lQegs1DCrmIx6KNzrbtWLh46Kzri12KQ5evyUVt2xxufvOcfDw_va9f6PZt87pebanjCnq6lCKAck55wWXFWanq4F1VcSGD1AIYHu1rsIj5wJz3C15L0HKpZCVFGcSc3E1z8byvIeTe7OOQjrjS8JJxqfE_jhSfKJdizinUpkvNwabRMDAnn8zkk0HW_PhkRhSJSZQRPu5C-hv9j-obsQRrXA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2912680002</pqid></control><display><type>article</type><title>A-ergodicity of probability measures on locally compact groups</title><source>Springer Nature</source><creator>Mustafayev, Heybetkulu</creator><creatorcontrib>Mustafayev, Heybetkulu</creatorcontrib><description>Let
G
be a locally compact group with the left Haar measure
m
G
and let
A
=
a
n
,
k
n
,
k
=
0
∞
be a strongly regular matrix. We show that if
μ
is a power bounded measure on
G
, then there exists an idempotent measure
θ
μ
such that
w*-
lim
n
→
∞
∑
k
=
0
∞
a
n
,
k
μ
k
=
θ
μ
.
If
μ
is a probability measure on a compact group
G
, then
w*-
lim
n
→
∞
∑
k
=
0
∞
a
n
,
k
μ
k
=
m
¯
H
,
where
H
is the closed subgroup of
G
generated by
supp
μ
and
m
¯
H
is the measure on
G
defined by
m
¯
H
E
:
=
m
H
E
∩
H
for every Borel subset
E
of
G
.</description><identifier>ISSN: 0003-889X</identifier><identifier>EISSN: 1420-8938</identifier><identifier>DOI: 10.1007/s00013-023-01938-y</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Mathematics ; Mathematics and Statistics ; Subgroups</subject><ispartof>Archiv der Mathematik, 2024, Vol.122 (1), p.47-57</ispartof><rights>Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-563e07cc7d326b2197fedcbb236e68301019df0a63ede1cdd42f6086576b639e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><creatorcontrib>Mustafayev, Heybetkulu</creatorcontrib><title>A-ergodicity of probability measures on locally compact groups</title><title>Archiv der Mathematik</title><addtitle>Arch. Math</addtitle><description>Let
G
be a locally compact group with the left Haar measure
m
G
and let
A
=
a
n
,
k
n
,
k
=
0
∞
be a strongly regular matrix. We show that if
μ
is a power bounded measure on
G
, then there exists an idempotent measure
θ
μ
such that
w*-
lim
n
→
∞
∑
k
=
0
∞
a
n
,
k
μ
k
=
θ
μ
.
If
μ
is a probability measure on a compact group
G
, then
w*-
lim
n
→
∞
∑
k
=
0
∞
a
n
,
k
μ
k
=
m
¯
H
,
where
H
is the closed subgroup of
G
generated by
supp
μ
and
m
¯
H
is the measure on
G
defined by
m
¯
H
E
:
=
m
H
E
∩
H
for every Borel subset
E
of
G
.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Subgroups</subject><issn>0003-889X</issn><issn>1420-8938</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKt_wNOC5-gkaZPsRShFq1DwouAtZJNs2bJt1mT3sP_eqSt48zAMwzzvfLyE3DK4ZwDqIQMAExQ4BiuFpuMZmbEFB6qxOicz7Auqdfl5Sa5y3iPNtSpn5HFFQ9pF37imH4tYF12Kla2a9lQegs1DCrmIx6KNzrbtWLh46Kzri12KQ5evyUVt2xxufvOcfDw_va9f6PZt87pebanjCnq6lCKAck55wWXFWanq4F1VcSGD1AIYHu1rsIj5wJz3C15L0HKpZCVFGcSc3E1z8byvIeTe7OOQjrjS8JJxqfE_jhSfKJdizinUpkvNwabRMDAnn8zkk0HW_PhkRhSJSZQRPu5C-hv9j-obsQRrXA</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Mustafayev, Heybetkulu</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2024</creationdate><title>A-ergodicity of probability measures on locally compact groups</title><author>Mustafayev, Heybetkulu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-563e07cc7d326b2197fedcbb236e68301019df0a63ede1cdd42f6086576b639e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Subgroups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mustafayev, Heybetkulu</creatorcontrib><collection>CrossRef</collection><jtitle>Archiv der Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mustafayev, Heybetkulu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A-ergodicity of probability measures on locally compact groups</atitle><jtitle>Archiv der Mathematik</jtitle><stitle>Arch. Math</stitle><date>2024</date><risdate>2024</risdate><volume>122</volume><issue>1</issue><spage>47</spage><epage>57</epage><pages>47-57</pages><issn>0003-889X</issn><eissn>1420-8938</eissn><abstract>Let
G
be a locally compact group with the left Haar measure
m
G
and let
A
=
a
n
,
k
n
,
k
=
0
∞
be a strongly regular matrix. We show that if
μ
is a power bounded measure on
G
, then there exists an idempotent measure
θ
μ
such that
w*-
lim
n
→
∞
∑
k
=
0
∞
a
n
,
k
μ
k
=
θ
μ
.
If
μ
is a probability measure on a compact group
G
, then
w*-
lim
n
→
∞
∑
k
=
0
∞
a
n
,
k
μ
k
=
m
¯
H
,
where
H
is the closed subgroup of
G
generated by
supp
μ
and
m
¯
H
is the measure on
G
defined by
m
¯
H
E
:
=
m
H
E
∩
H
for every Borel subset
E
of
G
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00013-023-01938-y</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0003-889X |
| ispartof | Archiv der Mathematik, 2024, Vol.122 (1), p.47-57 |
| issn | 0003-889X 1420-8938 |
| language | eng |
| recordid | cdi_proquest_journals_2912680002 |
| source | Springer Nature |
| subjects | Mathematics Mathematics and Statistics Subgroups |
| title | A-ergodicity of probability measures on locally compact groups |
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