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Inverse function ruleDifferentiable functionHomeomorphismKolmogorov continuity theoremUniform continuityIntermediate value theoremFundamental theorem of calculusTotal derivativeContinuous functionDirichlet conditionsHolomorphic functionDini's theoremStationary pointLebesgue differentiation theoremLebesgue integrationQuasiconvex functionConvolution theoremClosed graph theoremFixed-point theoremsLogarithmically concave functionLagrange inversion theoremLinear functionAntiderivativeGradient theoremEquicontinuitySmoothnessExtreme value theoremClosed range theoremFunction of a real variableBounded inverse theoremMeasurable functionConvex functionPartial derivativeEgorov's theoremMinkowski's theoremRolle's theoremGeneralized inverseContinuous linear operatorDominated convergence theoremMonotone convergence theoremChain ruleHilbert projection theoremIsolated pointCalculus on euclidean spaceSubadditivityTietze extension theoremInitial value problemLoopConvex conjugateLusin's theoremAlternating series testLefschetz fixed-point theoremSecond partial derivative testContinuous mapping theoremLinear differential equationInvertible matrixEuclidean domainTriangle inequalitySquare-integrable functionInjective functionRadial functionOrdinary differential equationDirichlet's approximation theoremCotangent bundleSchur-convex functionDivergence theoremBounded variationSimple pathSubderivativeCauchy's integral theoremLocal diffeomorphismInverse trigonometric functionsGradientMaximum theoremComplete metric spaceTangential and normal componentsIdentity theoremContinuumCharacteristic functionSkew gradientIntegral domainProper convex functionCenter of curvatureDirichlet problemRademacher's theoremConjugate gradient methodDerivative testSymmetric spaceDerivativeContact geometrySurjective functionMultiplicative inverseBanach fixed-point theoremDomainLipschitz domainAffine groupQuotient rulePositive linear functionalSchwarz reflection principleHyperbolic secant distribution