Envelope theorem

en

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Envelope theorem

Quality:

Envelope theorem - theorem in mathematics and economics. Article “Envelope theorem” in English Wikipedia has 38.7 points for quality (as of July 1, 2025). The article contains 29 references and 10 sections.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that (English) language version.

Since the creation of article “Envelope theorem”, its content was written by 60 registered users of English Wikipedia and edited by 131 registered Wikipedia users in all languages.

The article is cited 22 times in English Wikipedia and cited 47 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #37213 in October 2011
  • Global: #139579 in December 2018

The highest popularity rank from 2008:

  • Local (English): #177083 in October 2014
  • Global: #281683 in October 2010

There are 7 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1English (en)
Envelope theorem
38.7008
2German (de)
Umhüllungssatz
16.9258
3Chinese (zh)
包络定理
15.2699
4Russian (ru)
Теорема об огибающей
13.5424
5French (fr)
Théorème de l'enveloppe
12.2524
6Spanish (es)
Teorema de la envolvente
10.5921
7Italian (it)
Teorema dell'inviluppo
8.4621
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Envelope theorem" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Envelope theorem
681 343
2German (de)
Umhüllungssatz
85 428
3Chinese (zh)
包络定理
31 737
4Spanish (es)
Teorema de la envolvente
23 243
5Italian (it)
Teorema dell'inviluppo
20 694
6French (fr)
Théorème de l'enveloppe
11 792
7Russian (ru)
Теорема об огибающей
8 467
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2025

The most popular language versions of the article "Envelope theorem" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Envelope theorem
2 077
2Chinese (zh)
包络定理
249
3German (de)
Umhüllungssatz
242
4Spanish (es)
Teorema de la envolvente
86
5Italian (it)
Teorema dell'inviluppo
74
6French (fr)
Théorème de l'enveloppe
72
7Russian (ru)
Теорема об огибающей
37
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Envelope theorem" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Envelope theorem
60
2Italian (it)
Teorema dell'inviluppo
24
3German (de)
Umhüllungssatz
22
4French (fr)
Théorème de l'enveloppe
11
5Chinese (zh)
包络定理
6
6Spanish (es)
Teorema de la envolvente
4
7Russian (ru)
Теорема об огибающей
4
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2025

Language versions of the article "Envelope theorem" with the highest AI in June 2025
#LanguageAI awardRelative AI
1German (de)
Umhüllungssatz
1
2English (en)
Envelope theorem
0
3Spanish (es)
Teorema de la envolvente
0
4French (fr)
Théorème de l'enveloppe
0
5Italian (it)
Teorema dell'inviluppo
0
6Russian (ru)
Теорема об огибающей
0
7Chinese (zh)
包络定理
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Envelope theorem" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Envelope theorem
22
2German (de)
Umhüllungssatz
11
3Chinese (zh)
包络定理
6
4Spanish (es)
Teorema de la envolvente
4
5French (fr)
Théorème de l'enveloppe
2
6Italian (it)
Teorema dell'inviluppo
2
7Russian (ru)
Теорема об огибающей
0
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in June 2025:
English:
Global:
Popularity in all years:
English:
Global:
Authors in June 2025:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
deGerman
Umhüllungssatz
enEnglish
Envelope theorem
esSpanish
Teorema de la envolvente
frFrench
Théorème de l'enveloppe
itItalian
Teorema dell'inviluppo
ruRussian
Теорема об огибающей
zhChinese
包络定理

Popularity rank trends

Best Rank English:
#177083
10.2014
Global:
#281683
10.2010

AI rank trends

Best Rank English:
#37213
10.2011
Global:
#139579
12.2018

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Envelope theorem from Wikipedia articles about Shephards lemma, Envelope, Lagrange multiplier, Bellman equation and Danskins theorem. Whereas reading the article about Envelope theorem people most often go to Wikipedia articles on Hotellings lemma, Value function, Danskins theorem, Maximum theorem and Lagrange multiplier.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 5 March 2026

On 5 March 2026 in multilingual Wikipedia, Internet users most often read articles on the following topics: Iran, Ali Khamenei, 2026 Iran war, Jeffrey Epstein, Kurds, Strait of Hormuz, Yakovlev Yak-130, Donald Trump, Azerbaijan, Kristi Noem.

In English Wikipedia the most popular articles on that day were: Markwayne Mullin, Kristi Noem, 2026 Iran war, Ali Khamenei, Lou Holtz, Men's T20 World Cup, Iran, IRIS Dena, Corey Lewandowski, Deaths in 2026.

About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information