Haar measure (Q2782): Difference between revisions

@@ Property / Freebase ID @@
+/m/0b403
@@ Property / Freebase ID: /m/0b403 / rank @@
+Normal rank
@@ Property / Freebase ID: /m/0b403 / reference @@
+stated in: Freebase Data Dumps
publication date: 28 October 2013Timestamp +2013-10-28T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
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-Timestamp
++2013-10-28T00:00:00Z
-Timezone
++00:00
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+Gregorian
-Precision
+day
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@@ Property / MathWorld ID @@
+HaarMeasure
@@ Property / MathWorld ID: HaarMeasure / rank @@
+Normal rank
@@ Property / MathWorld ID: HaarMeasure / reference @@
+imported from Wikimedia project: Japanese Wikipedia
@@ Property / subclass of @@
+measure
@@ Property / subclass of: measure / rank @@
+Normal rank
@@ Property / named after @@
+Alfréd Haar
@@ Property / named after: Alfréd Haar / rank @@
+Normal rank
@@ Property / studied in @@
+group theory
@@ Property / studied in: group theory / rank @@
+Normal rank
@@ Property / studied in @@
+measure theory
@@ Property / studied in: measure theory / rank @@
+Normal rank
@@ Property / Microsoft Academic ID @@
+130805567
@@ Property / Microsoft Academic ID: 130805567 / rank @@
+Normal rank
@@ Property / instance of @@
+mathematical concept
@@ Property / instance of: mathematical concept / rank @@
+Normal rank
@@ Property / OpenAlex ID @@
+C130805567
@@ Property / OpenAlex ID: C130805567 / rank @@
+Normal rank
@@ Property / OpenAlex ID: C130805567 / reference @@
+stated in: OpenAlex
retrieved: 26 January 2022Timestamp +2022-01-26T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
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reference URL: https://docs.openalex.org/download-snapshot/snapshot-data-format
-Timestamp
++2022-01-26T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
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@@ Property / time of discovery or invention @@
+Timestamp +1933-00-00T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 year
Before 0
After 0
-Timestamp
++1933-00-00T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+year
 Before
 After
@@ Property / time of discovery or invention: 1933 / rank @@
+Normal rank
@@ Property / discoverer or inventor @@
+Alfréd Haar
@@ Property / discoverer or inventor: Alfréd Haar / rank @@
+Normal rank
@@ Property / nLab ID @@
+Haar integral
@@ Property / nLab ID: Haar integral / rank @@
+Normal rank
@@ Property / Encyclopedia of Mathematics article ID @@
+Haar_measure
@@ Property / Encyclopedia of Mathematics article ID: Haar_measure / rank @@
+Normal rank
@@ Property / defining formula @@
+ $\begin{matrix} μ : Borel (G) \to [0, \infty] \\ \forall g \in G, S \in Borel (G) : μ (g S) = μ (S) \\ μ (S) = \inf {μ (U) : S \subset U \in Open (G)} = \sup {μ (K) : S \supset K \in Comp (X) \end{matrix}$ 
\begin{aligned}&\mu\colon\operatorname{Borel}(G)\to[0,\infty]\\&\forall g\in G,S\in\operatorname{Borel}(G)\colon\mu(gS)=\mu(S)\\&\mu(S)=\inf\{\mu(U)\colon S\subset U\in\operatorname{Open}(G)\}=\sup\{\mu(K)\colon S\supset K\in\operatorname{Comp}(X)\end{aligned}
+Normal rank
@@ Property / in defining formula @@
+ $μ$ 
\mu
@@ Property / in defining formula: $μ$ / rank @@
+Normal rank
@@ Property / in defining formula: $μ$ / qualifier @@
+symbol represents: Haar measure
@@ Property / in defining formula @@
+ $G$ 
G
@@ Property / in defining formula: $G$ / rank @@
+Normal rank
@@ Property / in defining formula: $G$ / qualifier @@
+symbol represents: locally compact Hausdorff group
@@ Property / in defining formula @@
+ $Borel (G)$ 
\operatorname{Borel}(G)
@@ Property / in defining formula: $Borel (G)$ / rank @@
+Normal rank
@@ Property / in defining formula: $Borel (G)$ / qualifier @@
+symbol represents: Borel algebra
@@ Property / in defining formula @@
+ $Open (G)$ 
\operatorname{Open}(G)
@@ Property / in defining formula: $Open (G)$ / rank @@
+Normal rank
@@ Property / in defining formula: $Open (G)$ / qualifier @@
+symbol represents: topology
@@ Property / in defining formula @@
+ $\inf$ 
\inf
@@ Property / in defining formula: $\inf$ / rank @@
+Normal rank
@@ Property / in defining formula: $\inf$ / qualifier @@
+symbol represents: infimum
@@ Property / in defining formula @@
+ $\sup$ 
\sup
@@ Property / in defining formula: $\sup$ / rank @@
+Normal rank
@@ Property / in defining formula: $\sup$ / qualifier @@
+symbol represents: supremum
@@ Property / Mathematics Subject Classification ID @@
+H05
@@ Property / Mathematics Subject Classification ID: 20H05 / rank @@
+Normal rank
@@ Property / ScienceDirect topic ID @@
+mathematics/haar-measure
@@ Property / ScienceDirect topic ID: mathematics/haar-measure / rank @@
+Normal rank
@@ Property / ProofWiki ID @@
+Definition:Haar_Measure
@@ Property / ProofWiki ID: Definition:Haar_Measure / rank @@
+Normal rank