Revision #591 → #1379 · back to history
addedEuclidean normee23051f2837
addedp-norm in finite dimensions325e1575c0b8
addedMaximum norm (infinity-norm)fb6459086c7c
addedp-norm satisfies norm properties4a76e3074480
addedFinite-dimensional p-norm space is Banachff85f33989ad
addedEuclidean norm bounded by 1-normf19eeb645f43
addedp-norm decreases in pe0bb00a48f35
addedReverse inequality between p-norms (Cauchy–Schwarz)e3dbfaa353d7
addedGeneral p-norm comparison via Hölder63e931c5ba49
addedF-norm for 0<p<128137d41ac45
addedMetric on ℓ_p for 0<p<187d30dbb4dd7
addedFailure of local convexity in infinite-dim ℓ_p (0<p<1)cff29c79e77f
addedL^0 norm (Banach F-norm)b6779ed2088f
addedZero "norm" (Donoho)4ac134c57f61
addedZero "norm" is not a normd146a795d8f0
addedℓ^p sequence space05c488bab25f
addedℓ^p-norm on sequences8a7c277b3255
addedHarmonic sequence in ℓ^pc3f913ebe2eb
addedℓ^∞ norm and space359c26437b81
addedℓ^p is a Banach space001d246b702d
addedGeneral ℓ^p(I) space4c51f6873dec
addedEuclidean inner product on ℓ^2343e455b0455
addedℓ^p(I) as L^p with counting measure0664520985e0
addedL^p space (p finite)5756ebd7db6c
addedEqual almost everywhere593212f8c33c
addedEssentially bounded and L^∞be40646fd354
addedFunction equal to ∞ a.e.af149a6a91ca
addedp-norm relation |f|^p formula68dc700690f6
addedMinkowski inequality / triangle inequality for L^p972193f6c025
addedSeminorm property of L^p-seminorm08274f415d04
addedZero set of L^p-seminorm is independent of p16dd42d80135
addedQuotient space L^p758713aeb418
addedL^p-norm on quotientb3ae4436346a
addedRiesz–Fischer theorem (L^p is Banach)13c619eaba8c
addedℓ^p as special case of L^p997eb85a1ed6
addedL^2 is the only Hilbert L^p96aceac03015
addedInner product on L^26693fc807c0f
addedEvery Hilbert space is isometric to some ℓ^2(I)cef5d354d1ce
addedL^∞ is a commutative C*-algebrac52408ba356e
addedL^p quasi-norm for 0<p<11f39ab3835df
addedCompleteness of L^p metric (0<p<1)ca567f64b87a
addedReverse Minkowski inequalitycbeca2a32e11
addedClarkson's inequalities and uniform convexitye1d41aecfb97
addedL^p (0<p<1) is an F-space, not locally convexab0cb48d7d5a
addedTrivial dual of L^p for 0<p<18650ebcc905d
addedHölder's inequality21458d17eac2
addedGeneralized Minkowski inequality5e0dc6937358
addedAtomic decomposition for L^p3273c04303fd
addedExplicit construction of atomic decomposition536314592ed6
addedLayer-cake formula for L^p-norm36cf5eb5ab36
addedDual of L^p is L^q59d56e25e684
addedReflexivity of L^p for 1<p<∞1d5d8bf104f2
addedDual of L^1 is L^∞ (sigma-finite)dfe8b13945d2
addedDual of L^∞88b78501d1fd
addedEmbedding criterion for L^p ⊂ L^q (p<q)77ab28f536bc
addedEmbedding criterion for L^q ⊂ L^p (p<q)f372f6c3d51d
addedContinuity of embedding via closed graph073c36840ef1
addedOptimal constant of embedding1059d4281131
addedDensity of integrable simple functions8722df80874f
addedUrysohn approximation in normal spacesc77d10da61eb
addedDensity of continuous integrable functions95d0536d614b
addedContinuous compactly supported functions dense in L^p(R^n)604f8b55f218
addedGrothendieck closed subspace theoremedeedcdfa088
addedHausdorff–Young inequalityd1c54c63e6cb
addedFourier transform fails to map into L^q for p>24449137c5675
addedEvery Hilbert space is isometric to ℓ^2(B)b4848acb8d61
addedDistribution functionce6d8c0a6a5d
addedMarkov's inequality bound45410e37db2d
addedWeak L^p space5a61962c8482
addedWeak L^p quasi-norm6e1b8cef45cc
addedWeak L^p coincides with Lorentz space0b4ff0310f2b
addedWeak L^p quasi-triangle inequality89ec921e51df
addedCompleteness of weak L^p1b27ff870dcb
addedWeak L^p comparable to L^p norm; Banach for p>1e3b28eabe797
addedMarcinkiewicz interpolation theorem4139c631e858
addedWeighted L^p space7cae1bf90b8b
addedMuckenhoupt's theorem9c55253bfda6
addedIntrinsic L^p on manifolds673b58e27a12
addedVector-valued L^p via Bochner/Pettisbe98555e016e
addedVector-valued L^p via tensor productse78699271b0f
addedGrothendieck nuclearity theorem for vector-valued L^pee88456a8962
addedL^0 space of measurable functionsc102fc7ff071
addedL^0 is a TVS iff μ has no atoms condition28aac0925102
addedLocal convergence in measure is an F-space5bfbba946818
addedLévy metric on L^08d3603f3a17f
addedL^0 isomorphism for infinite Lebesgue measure748e85b2edd8