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The 33 pages that link to Real analysis, each with the reason it gives.

• Real numberNarrower topic: Real analysis develops the calculus and convergence theory grounded in the real continuum.

• Complex analysisCompared with: Complex differentiability imposes constraints absent from ordinary real differentiability.

• Augustin-Louis CauchyNarrower topic: Cauchy’s proofs helped make this field more rigorous.

• Cauchy sequenceNarrower topic: Cauchy sequences became a central tool in making analysis rigorous.

• Pointwise convergenceNarrower topic: Pointwise convergence is a central mode of convergence studied in real analysis.

• Intermediate value theoremNarrower topic: The theorem became a foundational result in the rigorous development of this subject.

• Karl WeierstrassNarrower topic: His exacting treatment of limits and continuity helped shape this field's foundations.

• Cantor setNarrower topic: The construction became a standard example in the rigorous study of real-line sets and continuity.

• Contour integrationCompared with: Real-variable techniques offer an alternative when no useful complex contour exists.

• Bernard BolzanoNarrower topic: Bolzano sought rigorous foundations for the central concepts of this field.

• Dedekind cutNarrower topic: Its foundational arguments depend on the completeness of the real numbers cuts construct.

• Henri LebesgueNarrower topic: Lebesgue’s work transformed the foundations and tools of this mathematical field.

• Mathematical analysisBroader topic: It is the foundational subfield focused on real-valued functions and the real line.

• Rolle's theoremNarrower topic: The theorem's standard modern form depends on the precise concepts developed in real analysis.

• Number lineNarrower topic: Its central objects and order properties are grounded in the real line.

• Giuseppe PeanoNarrower topic: Peano’s early research addressed rigorous questions in analysis and integration.

• Nonmeasurable setNarrower topic: Nonmeasurable sets reveal why integration is restricted to carefully chosen domains.

• Pure mathematicsRelated: It turns calculus into a theory grounded in precise definitions and proofs.

• Tonelli's theoremNarrower topic: The theorem is a foundational result in measure-theoretic real analysis.

• Monotone convergence theoremNarrower topic: The theorem is a basic consequence of real-number order and completeness.

• General topologyRelated: Its familiar continuity and convergence concepts extend naturally to topological spaces.

• Heine–Cantor theoremNarrower topic: The theorem is a foundational result connecting continuity with compactness in analysis.

• John Edensor LittlewoodNarrower topic: Littlewood’s inequalities and convergence results grew from questions in real analysis.

• Discrete mathematicsCompared with: Its central objects are continuous spaces and limiting processes.

• Abel's testNarrower topic: Abel's test is a standard theorem within the study of convergence in real analysis.

• Aleksandr LyapunovNarrower topic: Rigorous estimates and limiting arguments underpin both his stability and probability results.

• Young's inequality for productsNarrower topic: Young's inequality became a standard tool in the development of rigorous analysis.

• Stolz–Cesàro theoremNarrower topic: The theorem belongs to the classical theory of sequence limits.

• Denjoy–Luzin theoremNarrower topic: The theorem emerged from the study of how derivatives behave beyond ordinary continuity.

• Function of a real variableNarrower topic: It provides the broader theory of convergence and continuity for real-variable functions.

• Infimum and supremumNarrower topic: Completeness through suprema underpins many existence proofs in real analysis.

• Levinson's inequalityNarrower topic: The inequality is a derivative-based theorem about real-valued functions.

• Standard part functionCompared with: Standard parts translate certain hyperreal arguments into real-analysis results.