Strongly measurable function

Strong measurability has a number of different meanings, some of which are explained below.For a function f with values in a Banach space (or Fréchet space), strong measurability usually means Bochner measurability.of continuous linear operators from X to Y, then often strong measurability means that the operator f(x) is Bochner measurable for each fixed x in the domain of f, whereas the Bochner measurability of f is called uniform measurability (cf.A family of bounded linear operators combined with the direct integral is strongly measurable, when each of the individual operators is strongly measurable.This algebra-related article is a stub.

Banach spaceFréchet spaceBochner measurabilitycontinuous linear operatorsuniformly continuousstrongly continuousdirect integralsemigroupFunctional analysistopicsglossaryBanachFréchetHilbertHölderNuclearOrliczSchwartzSobolevTopological vectorBarrelledCompleteLocally convexReflexiveSeparableHahn–BanachRiesz representationClosed graphUniform boundedness principleKrein–MilmanMin–maxGelfand–NaimarkBanach–AlaogluAdjointBoundedCompactHilbert–SchmidtNormalTrace classTransposeUnboundedUnitaryBanach algebraC*-algebraSpectrum of a C*-algebraOperator algebraGroup algebra of a locally compact groupVon Neumann algebraInvariant subspace problemMahler's conjectureHardy spaceSpectral theory of ordinary differential equationsHeat kernelIndex theoremCalculus of variationsFunctional calculusIntegral linear operatorJones polynomialTopological quantum field theoryNoncommutative geometryRiemann hypothesisDistributionGeneralized functionsApproximation propertyBalanced setChoquet theoryWeak topologyBanach–Mazur distanceTomita–Takesaki theoryAnalysistopological vector spacesAbstract Wiener spaceClassical Wiener spaceBochner spaceConvex seriesCylinder set measureInfinite-dimensional vector functionMatrix calculusVector calculusDerivativesDifferentiable vector–valued functions from Euclidean spaceDifferentiation in Fréchet spacesFréchet derivativeFunctional derivativeGateaux derivativeDirectionalGeneralizations of the derivativeHadamard derivativeHolomorphicQuasi-derivativeBesov measureCanonical GaussianClassical Wiener measureMeasureset functionsProjection-valuedVectorBochnerWeaklymeasurable functionRadonifying functionIntegralsDunfordGelfand–Pettis/WeakRegulatedPaley–WienerCameron–Martin theoremInverse function theoremNash–Moser theoremFeldman–Hájek theoremNo infinite-dimensional Lebesgue measureSazonov's theoremStructure theorem for Gaussian measuresCrinkled arcCovariance operatorBorel functional calculusContinuous functional calculusHolomorphic functional calculusBanach manifoldbundleConvenient vector spaceFréchet manifoldHilbert manifoldalgebra