[Merged by Bors] - feat: Order-connected sets in ℝⁿ are null-measurable#13633
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[Merged by Bors] - feat: Order-connected sets in ℝⁿ are null-measurable#13633YaelDillies wants to merge 4 commits intomasterfrom
ℝⁿ are null-measurable#13633YaelDillies wants to merge 4 commits intomasterfrom
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PR summary 8d30fcbe02Import changesNo significant changes to the import graph
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YaelDillies
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Jun 8, 2024
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Jun 8, 2024
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Prove that the frontier of an order-connected set in `ℝⁿ` (with the `∞`-metric, but it doesn't actually matter) has measure zero. As a corollary, antichains in `ℝⁿ` have measure zero. This is not so trivial as one might think. The proof Kexing and I came up with involves the Lebesgue density theorem. Partially forward-port leanprover-community/mathlib3#16976
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🚀 Pull request has been placed on the maintainer queue by JasonKYi. |
ℝⁿ are measurableℝⁿ are null-measurable
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Prove that the frontier of an order-connected set in `ℝⁿ` (with the `∞`-metric, but it doesn't actually matter) has measure zero. As a corollary, antichains in `ℝⁿ` have measure zero. This is not so trivial as one might think. The proof Kexing and I came up with involves the Lebesgue density theorem. Partially forward-port leanprover-community/mathlib3#16976
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ℝⁿ are null-measurableℝⁿ are null-measurable
AntoineChambert-Loir
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Prove that the frontier of an order-connected set in `ℝⁿ` (with the `∞`-metric, but it doesn't actually matter) has measure zero. As a corollary, antichains in `ℝⁿ` have measure zero. This is not so trivial as one might think. The proof Kexing and I came up with involves the Lebesgue density theorem. Partially forward-port leanprover-community/mathlib3#16976
grunweg
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Prove that the frontier of an order-connected set in `ℝⁿ` (with the `∞`-metric, but it doesn't actually matter) has measure zero. As a corollary, antichains in `ℝⁿ` have measure zero. This is not so trivial as one might think. The proof Kexing and I came up with involves the Lebesgue density theorem. Partially forward-port leanprover-community/mathlib3#16976
kbuzzard
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Jun 26, 2024
Prove that the frontier of an order-connected set in `ℝⁿ` (with the `∞`-metric, but it doesn't actually matter) has measure zero. As a corollary, antichains in `ℝⁿ` have measure zero. This is not so trivial as one might think. The proof Kexing and I came up with involves the Lebesgue density theorem. Partially forward-port leanprover-community/mathlib3#16976
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Prove that the frontier of an order-connected set in
ℝⁿ(with the∞-metric, but it doesn't actually matter) has measure zero. As a corollary, antichains inℝⁿhave measure zero.This is not so trivial as one might think. The proof Kexing and I came up with involves the Lebesgue density theorem.
Partially forward-port leanprover-community/mathlib3#16976
(𝓝[<] x).NeBotinstances forProd,Pi,OrderDual#13642