Haar measure

Summary

Haar measure is a mathematical concept^[1]. It ranks in the top 8% of mathematical_concept entities by monthly Wikipedia readership (258 views/month).^[2]

Key Facts

• Haar measure is credited with the discovery of Alfréd Haar^[3].
• Haar measure's instance of is recorded as mathematical concept^[4].
• Alfréd Haar is named after Haar measure^[5].
• Haar measure's subclass of is recorded as measure^[6].
• Haar measure's time of discovery or invention is recorded as +1933-00-00T00:00:00Z^[7].
• Haar measure's Freebase ID is recorded as /m/0b403^[8].
• Haar measure's defining formula is recorded as \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}^[9].
• Haar measure's studied by is recorded as group theory^[10].
• Haar measure's studied by is recorded as measure theory^[11].
• Haar measure's MathWorld ID is recorded as HaarMeasure^[12].
• Haar measure's Mathematics Subject Classification ID is recorded as 20H05^[13].
• Haar measure's nLab ID is recorded as Haar integral^[14].
• Haar measure's maintained by WikiProject is recorded as WikiProject Mathematics^[15].
• Haar measure's Microsoft Academic ID is recorded as 130805567^[16].
• Haar measure's ProofWiki ID is recorded as Definition:Haar_Measure^[17].
• Haar measure's in defining formula is recorded as \mu^[18].
• Haar measure's in defining formula is recorded as G^[19].
• Haar measure's in defining formula is recorded as \operatorname{Borel}(G)^[20].
• Haar measure's in defining formula is recorded as \operatorname{Open}(G)^[21].
• Haar measure's in defining formula is recorded as \inf^[22].
• Haar measure's in defining formula is recorded as \sup^[23].
• Haar measure's Encyclopedia of Mathematics article ID is recorded as Haar_measure^[24].
• Haar measure's OpenAlex ID is recorded as C130805567^[25].
• Haar measure's ScienceDirect topic ID is recorded as mathematics/haar-measure^[26].

Body

Works and Contributions

Haar measure is credited with the discovery of Alfréd Haar^[3].

Why It Matters

Haar measure ranks in the top 8% of mathematical_concept entities by monthly Wikipedia readership (258 views/month).^[2] It has Wikipedia articles in 18 language editions, a strong signal of global cultural recognition.^[27] It is known by 13 alternative names across languages and contexts.^[28]