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dominated convergence theorem

theorem that, for a sequence of functions bounded in absolute value by an integrable function, then almost everywhere pointwise convergence implies L¹ convergence
Intangible theorem Q1067156
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dominated convergence theorem

Summary

dominated convergence theorem is a theorem[1]. It ranks in the top 4% of theorem entities by monthly Wikipedia readership (373 views/month).[2]

Key Facts

  • dominated convergence theorem's instance of is recorded as theorem[3].
  • Henri Lebesgue is named after dominated convergence theorem[4].
  • dominated convergence theorem's part of is recorded as list of theorems[5].
  • dominated convergence theorem's Freebase ID is recorded as /m/01zcw3[6].
  • dominated convergence theorem's defining formula is recorded as \left(\exists g\in L^1(X)\forall i\colon |f_i(x)|<g(x)\right)\land\left(\forall x\in X\colon\lim_{i\to\infty}f_i(x)=f(x)\right)\implies (f_i)_{i\in\mathbb N} \xrightarrow{L^1} f<sup id="cite-C10" class="cite-ref" title="dominated convergence theorem — defining formula (P2534): \left(\exists g\in L^1(X)\forall i\colon |f_i(x)|[7].
  • dominated convergence theorem's studied by is recorded as calculus[8].
  • dominated convergence theorem's studied by is recorded as measure theory[9].
  • dominated convergence theorem's MathWorld ID is recorded as LebesguesDominatedConvergenceTheorem[10].
  • dominated convergence theorem's Quora topic ID is recorded as Dominated-Convergence-Theorem[11].
  • dominated convergence theorem's maintained by WikiProject is recorded as WikiProject Mathematics[12].
  • dominated convergence theorem's Microsoft Academic ID is recorded as 38487692[13].
  • dominated convergence theorem's ProofWiki ID is recorded as Lebesgue's_Dominated_Convergence_Theorem[14].
  • dominated convergence theorem's OpenAlex ID is recorded as C38487692[15].
  • dominated convergence theorem's ScienceDirect topic ID is recorded as mathematics/dominated-convergence-theorem[16].
  • dominated convergence theorem's ScienceDirect topic ID is recorded as mathematics/lebesgue-dominated-convergence-theorem[17].
  • dominated convergence theorem's Digital Library of Mathematical Functions ID is recorded as 1.9.E71[18].
  • dominated convergence theorem's Great Russian Encyclopedia portal ID is recorded as teorema-lebega-o-mazhoriruemoi-skhodimosti-627477[19].

Why It Matters

dominated convergence theorem ranks in the top 4% of theorem entities by monthly Wikipedia readership (373 views/month).[2] It has Wikipedia articles in 17 language editions, a strong signal of global cultural recognition.[20] It is known by 19 alternative names across languages and contexts.[21]

Related Entities

Henri Lebesgue

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] ↑ . wikidata.org.
  4. [6] ↑ . Freebase Data Dumps. wikidata.org.
  5. [7] ↑ . wikidata.org.
  6. [8] ↑ . wikidata.org.
  7. [9] ↑ . wikidata.org.
  8. [10] ↑ . wikidata.org.
  9. [11] ↑ . Quora. wikidata.org.
  10. [12] ↑ . wikidata.org.
  11. [13] ↑ . wikidata.org.
  12. [14] ↑ . wikidata.org.
  13. [15] ↑ . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.
  14. [16] ↑ . wikidata.org.
  15. [17] ↑ . wikidata.org.
  16. [18] ↑ . wikidata.org.
  17. [19] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [20] ↑ . Wikidata sitelinks. wikidata.org.
  3. [21] ↑ . 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). dominated convergence theorem. Retrieved May 3, 2026, from https://4ort.xyz/entity/dominated-convergence-theorem
MLA “dominated convergence theorem.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/dominated-convergence-theorem.
BibTeX @misc{4ortxyz_dominated-convergence-theorem_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{dominated convergence theorem}}, year = {2026}, url = {https://4ort.xyz/entity/dominated-convergence-theorem}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): dominated convergence theorem — https://4ort.xyz/entity/dominated-convergence-theorem (retrieved 2026-05-03)

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