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Mathematics
Calculus
Is Lebesgue Outer Measure Uniquely Characterized by These Requirements?
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[QUOTE="Diophantus, post: 1146705, member: 41621"] It is a fact that Lebesgue measure is characterised uniquely by the five requirements: 1 - measure of empty set = 0 2 - monotonicity 3 - measure = length for intervals 4 - translation invariance 5 - countable additivity It is also true that Lebesgue outer measure satisfies: 1 - measure of empty set = 0 2 - monotonicity 3 - measure = length for intervals 4 - translation invariance 5 - countable [I]subadditivity[/I] but I'm dying to know whether these requirements actually [I]characterise[/I] Lebesgue outer measure [I]uniquely[/I]. [/QUOTE]
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Forums
Mathematics
Calculus
Is Lebesgue Outer Measure Uniquely Characterized by These Requirements?
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