Direct integral

en

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Direct integral

Quality:

Direct integral - generalization of the concept of direct sum. Article “Direct integral” in English Wikipedia has 18 points for quality (as of July 1, 2025). The article contains 1 references and 8 sections. The article also contains templates indicating quality issues, therefore its score was reduced by 0.95 points.

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 “Direct integral”, its content was written by 28 registered users of English Wikipedia and edited by 31 registered Wikipedia users in all languages.

The article is cited 123 times in English Wikipedia and cited 124 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #78577 in December 2004
  • Global: #151237 in December 2004

The highest popularity rank from 2008:

  • Local (English): #259071 in September 2017
  • Global: #444815 in September 2017

There are 2 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)
Direct integral
18.0062
2Portuguese (pt)
Integral direta
14.0138
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 "Direct integral" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Direct integral
100 889
2Portuguese (pt)
Integral direta
647
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 "Direct integral" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Direct integral
452
2Portuguese (pt)
Integral direta
14
More...

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

The highest AI

Language versions of the article "Direct integral" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Direct integral
28
2Portuguese (pt)
Integral direta
3
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 "Direct integral" with the highest AI in June 2025
#LanguageAI awardRelative AI
1English (en)
Direct integral
0
2Portuguese (pt)
Integral direta
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 "Direct integral" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Direct integral
123
2Portuguese (pt)
Integral direta
1
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
enEnglish
Direct integral
ptPortuguese
Integral direta

Popularity rank trends

Best Rank English:
#259071
09.2017
Global:
#444815
09.2017

AI rank trends

Best Rank English:
#78577
12.2004
Global:
#151237
12.2004

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Direct integral from Wikipedia articles about Von Neumann algebra, Spectral theorem, Functional calculus, Projection-valued measure and List of things named after John von Neumann. Whereas reading the article about Direct integral people most often go to Wikipedia articles on Direct sum, Artin–Wedderburn theorem, John von Neumann, System of imprimitivity and Von Neumann algebra.

Cumulative results of quality and popularity of the Wikipedia article

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

News from 28 January 2026

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In English Wikipedia the most popular articles on that day were: Ajit Pawar, Border 2, Sharad Pawar, Killing of Alex Pretti, Ilhan Omar, Sunetra Pawar, Todd Monken, Kristi Noem, Wonder Man (miniseries), Gregory Bovino.

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