SHMARQL

Haar measure

<http://www.wikidata.org/entity/Q1162676>

left-invariant (or right-invariant) measure on locally compact topological group
rdfs:label
"Haar measure"@en
skos:altLabel
"Haar integral"@en
"left Haar measure"@en
"right Haar measure"@en
schema:description
"left-invariant (or right-invariant) measure on locally compact topological group"@en
schema:dateModified "2026-09-06T20:24:45+00:00"^^xsd:dateTime
schema:version 2541298347
wikibase:identifiers 9
wikibase:sitelinks 21
wikibase:statements 24
p:P10283 wd:statement/Q1162676-A206A6ED-DE8A-4C23-95D7-BFF831FC2043
p:P10376 wd:statement/Q1162676-de766aff-4308-2de8-842e-bc45ee72c6f1
p:P138 wd:statement/Q1162676-345a22ab-4f94-4cee-4188-617d224d2b41
p:P2534 wd:statement/Q1162676-a1c197d7-4d6c-f617-4307-9e6780447209
p:P2579 wd:statement/Q1162676-2a132e60-495f-a111-f4bd-458332db2ee6
wd:statement/Q1162676-FB62AADA-7F74-4E15-B101-65E7BC3DAB81
p:P279 wd:statement/Q1162676-1B9BCD8F-E4E3-4C97-AA29-0C9D77FECF50
p:P2812 wd:statement/Q1162676-89396092-07B8-4992-8513-A86EF3914424
p:P31 wd:statement/Q1162676-b710eb2f-4809-c03d-ce51-2b9031f306a3
p:P3285 wd:statement/Q1162676-41DB4CE6-5FE2-4EFA-99C0-1B3D5B432E33
p:P4215 wd:statement/Q1162676-9e315388-4665-3219-4e6c-a4eb1d2a5961
p:P575 wd:statement/Q1162676-7667df6e-4262-e758-6299-9abddebb8a97
p:P61 wd:statement/Q1162676-4c3fe1ef-4b1c-cf7e-1747-5cf91870f09c
p:P6104 wd:statement/Q1162676-FC9F7BD2-7792-439E-9F57-D694C9D685F4
p:P6366 wd:statement/Q1162676-ECD0502F-AD40-48C2-89DA-18830BAD97CC
p:P646 wd:statement/Q1162676-592843AC-5927-4DE2-8B12-2E264E6E9E1F
p:P6781 wd:statement/Q1162676-ed40faa8-4832-b476-f4b1-36b46e98f922
p:P7235 wd:statement/Q1162676-0d2d5b8d-4932-5dca-b26e-8aa4ad42abe0
wd:statement/Q1162676-5d4df425-4d00-e3dd-bee0-8e74f791f205
wd:statement/Q1162676-7e0c059b-4bd3-184b-7299-18408abbf321
wd:statement/Q1162676-7f10a44c-4788-1a51-a7d8-83111aa3510d
wd:statement/Q1162676-918c44a3-420d-3287-6732-1f3534a3d862
wd:statement/Q1162676-b12e0b80-482a-bd87-0f04-257d778849d4
p:P7554 wd:statement/Q1162676-5a7f858e-4a3a-c302-5476-92ad5df7bf72
p:direct-normalized/P3285 <http://msc2010.org/resources/MSC/2010/20H05>
p:direct-normalized/P6366 <https://makg.org/entity/130805567>
wdt:P10283 "C130805567"
wdt:P10376 "mathematics/haar-measure"
wdt:P138 Alfréd Haar
wdt:P2534 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>&#x03BC;</mi><mo stretchy="false">&#x003A;</mo><mi data-mjx-texclass="OP" mathvariant="normal">Borel</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>G</mi><mo stretchy="false">)</mo><mo stretchy="false" accent="false">&#x2192;</mo><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mi mathvariant="normal">&#x221E;</mi><mo stretchy="false">]</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi mathvariant="normal">&#x2200;</mi><mi>g</mi><mo stretchy="false">&#x2208;</mo><mi>G</mi><mo>,</mo><mi>S</mi><mo stretchy="false">&#x2208;</mo><mi data-mjx-texclass="OP" mathvariant="normal">Borel</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>G</mi><mo stretchy="false">)</mo><mo stretchy="false">&#x003A;</mo><mi>&#x03BC;</mi><mo stretchy="false">(</mo><mi>g</mi><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>&#x03BC;</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>&#x03BC;</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>inf</mi><mo>&#x2061;</mo><mo fence="false" stretchy="false">{</mo><mi>&#x03BC;</mi><mo stretchy="false">(</mo><mi>U</mi><mo stretchy="false">)</mo><mo stretchy="false">&#x003A;</mo><mi>S</mi><mo stretchy="false">&#x2282;</mo><mi>U</mi><mo stretchy="false">&#x2208;</mo><mi data-mjx-texclass="OP" mathvariant="normal">Open</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>G</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo><mo stretchy="false">=</mo><mi>sup</mi><mo>&#x2061;</mo><mo fence="false" stretchy="false">{</mo><mi>&#x03BC;</mi><mo stretchy="false">(</mo><mi>K</mi><mo stretchy="false">)</mo><mo stretchy="false">&#x003A;</mo><mi>S</mi><mo stretchy="false">&#x2283;</mo><mi>K</mi><mo stretchy="false">&#x2208;</mo><mi data-mjx-texclass="OP" mathvariant="normal">Comp</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P2579 measure theory
group theory
wdt:P279 measure
wdt:P2812 "HaarMeasure"
wdt:P31 mathematical concept
wdt:P3285 "20H05"
wdt:P4215 "Haar integral"
wdt:P575 "1933-01-01T00:00:00+00:00"^^xsd:dateTime
wdt:P61 Alfréd Haar
wdt:P6104 WikiProject Mathematics
wdt:P6366 "130805567"
wdt:P646 "/m/0b403"
wdt:P6781 "Definition:Haar_Measure"
wdt:P7235 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi data-mjx-texclass="OP" mathvariant="normal">Borel</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>G</mi><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi data-mjx-texclass="OP" mathvariant="normal">Open</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>G</mi><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>&#x03BC;</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>G</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>inf</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>sup</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P7554 "Haar_measure"
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