Revision #586 → #1356 · back to history
addedLength of an intervalfec6f5e38f27
addedLebesgue outer measure (one dimension)1b8423ca195f
addedLebesgue outer measure in higher dimensionsc877d813819a
addedCarathéodory criterion38a5315e53eb
addedLebesgue-measurable set12c1cf1092d2
addedMeasurable sets form a σ-algebra24fee46c90a2
addedLebesgue measureebf68e560338
addedNon-measurable sets exist in ZFCdca0f59d1a9a
addedMeasure of a closed intervale1c6a198aa7a
addedOpen interval has same measure as closedbcbf35eb0552
addedMeasure of a Cartesian product of intervals4d904fa3d317
addedEvery Borel set is Lebesgue-measurablefce2f1dc94ae
addedMeasurable sets that are not Borel7da38e929713
addedCountable set has measure zero7002bfac4ee7
addedAlgebraic numbers have measure zero19941bb8d82e
addedCantor set and Liouville numbers have measure zerod5e704165ae4
addedAxiom of determinacy implies all sets measurable8b4c79a1f265
addedVitali sets are non-measurablece4431830f00
addedOsgood curves have positive measureb5e3af9c7baf
addedA line in R^n has measure zerof15c4f5beaba
addedProper hyperplane has measure zerof881b801a70f
addedVolume of an n-ballaea760a8ef41
addedCartesian product of intervals is measurable567efa7d32a9
addedCountable additivity2fbc11da5c9e
addedComplement of a measurable set is measurable507b9800bf86
addedNon-negativity of the measure30b98df48ad6
addedMonotonicity7f4c0b64c7d6
addedClosure under countable unions and intersections77d62a28f224
addedOpen, closed, and Borel sets are measurable3c86e1c95379
addedSqueeze between open and closed sets (regularity)63542a3f317a
addedSqueeze between Gδ and Fσ setsae6ad7c94b47
addedLebesgue measure is a Radon measure69babd50afbe
addedStrictly positive on open sets; full supportf4ff559b8f15
addedCompleteness: subsets of null sets are null37b3bdaee7d0
addedTranslation invariance5f6de3dd6720
addedBehavior under dilationfe3b39b3c5fb
addedBehavior under linear transformations1e32c28bfc08
addedLebesgue measure is σ-finite24b156391d05
addedNull set129412a7c1f9
addedAll countable sets are null8293acb11301
addedHausdorff dimension less than n implies null26915518fc35
addedSmith–Volterra–Cantor set9645e4617d93
addedBox in R^n and its volume7365bdf85528
addedNon-measurable sets follow from the axiom of choicebfc47a2a2749
addedVitali theorem1273e95455fe
addedBanach–Tarski paradox5ce872672bb5
addedSolovay's independence resultb9c342319082
addedBorel measure agrees with Lebesgue measure1ca7f0b1c932
addedMore measurable sets than Borel setsd5743eba5bfa
addedLebesgue measure is a locally finite Borel measure7a98b62492d4
addedBorel measure translation-invariant but not complete2dd6b4446544
addedHaar measure generalizes Lebesgue measure8d1015978982
addedHausdorff measure generalizes Lebesgue measuree30572937c2a
addedNo infinite-dimensional Lebesgue measure8a458a0602c7