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All Analysis

Proved results about limits, continuity and the functions built from them. Belongs here: theorems in real, complex or functional analysis. Does not belong here: results that remain open, filed as conjectures.

Fatou's Lemma

Fejer's Theorem

Frankova-Helly Selection Theorem

Fredholm Alternative

Fubini's Theorem

Fubini's Theorem on Differentiation

Fundamental Theorem of Calculus

Gauss-Lucas Theorem

Goursat's Theorem

Gradient Theorem

Green's Theorem

Gronwall's Inequality

Hadamard Three-Lines Theorem

Hahn-Banach Theorem

Heine-Borel Theorem

Helly's Selection Theorem

Identity Theorem (Complex Analysis)

Implicit Function Theorem

Increment Theorem

Interior Extremum Theorem

Intermediate Value Theorem

Inverse Function Theorem

Kolmogorov-Arnold Representation Theorem

Krein-Milman Theorem

Lax-Milgram Theorem

Lebesgue Differentiation Theorem

Liouville's Theorem (Complex Analysis)

Lusin's Theorem

Malgrange Preparation Theorem

Maximum Modulus Principle

Maximum Theorem

Mean Value Theorem

Mercer's Theorem

Mergelyan's Theorem

Minkowski's Inequality

Mittag-Leffler Theorem

Monotone Convergence Theorem

Montel's Theorem

Morera's Theorem

Multiplication Theorem

Muntz-Szasz Theorem

Namioka's Theorem

Open Mapping Theorem (Complex Analysis)

Open Mapping Theorem (Functional Analysis)

Parseval's Theorem

Peano Existence Theorem

Phragmen-Lindelof Principle

Picard Theorem

Picard-Lindelof Theorem

Plancherel Theorem