Fatou's lemma

inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions
Thing lemma Q1068118
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Fatou's lemma

Summary

Fatou's lemma is a lemma[1]. It ranks in the top 6% of lemma entities by monthly Wikipedia readership (194 views/month).[2]

Key Facts

  • Fatou's lemma's instance of is recorded as lemma[3].
  • Pierre Fatou is named after Fatou's lemma[4].
  • Fatou's lemma's Freebase ID is recorded as /m/01qnct[5].
  • Fatou's lemma's defining formula is recorded as \int X(\liminf{n\to\infty}f_n)\,\mathrm d\mu \le \liminf_{n\to \infty}\int_Xf_n\,\mathrm d\mu[6].
  • Fatou's lemma's maintained by WikiProject is recorded as WikiProject Mathematics[7].
  • Fatou's lemma's Microsoft Academic ID is recorded as 42457614[8].
  • Fatou's lemma's Encyclopedia of Mathematics article ID is recorded as Fatou_theorem_(on_Lebesgue_integrals)[9].
  • Fatou's lemma's Treccani's Enciclopedia della Matematica ID is recorded as lemma-di-fatou[10].
  • Fatou's lemma's ScienceDirect topic ID is recorded as mathematics/fatous-lemma[11].
  • Fatou's lemma's Great Russian Encyclopedia portal ID is recorded as lemma-fatu-e6988f[12].

Why It Matters

Fatou's lemma ranks in the top 6% of lemma entities by monthly Wikipedia readership (194 views/month).[2] It has Wikipedia articles in 16 language editions, a strong signal of global cultural recognition.[13] It is known by 4 alternative names across languages and contexts.[14]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . Freebase Data Dumps. wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [13] . Wikidata sitelinks. wikidata.org.
  3. [14] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Fatou's lemma. Retrieved May 3, 2026, from https://4ort.xyz/entity/fatou-s-lemma
MLA “Fatou's lemma.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/fatou-s-lemma.
BibTeX @misc{4ortxyz_fatou-s-lemma_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Fatou's lemma}}, year = {2026}, url = {https://4ort.xyz/entity/fatou-s-lemma}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Fatou's lemma — https://4ort.xyz/entity/fatou-s-lemma (retrieved 2026-05-03)

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