[Merged by Bors] - feat(analysis/normed_space/finite_dimension): extending partially defined Lipschitz functions #11530
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| lemma lipschitz_on_with.extend_pi [pseudo_metric_space α] [fintype ι] | ||
| {f : α → (ι → ℝ)} {s : set α} {K : ℝ≥0} | ||
| (hf : lipschitz_on_with K f s) : | ||
| ∃ g : α → (ι → ℝ), lipschitz_with K g ∧ eq_on f g s := |
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I believe this is also true for infinite ι with the l-infinity norm, with essentially the same proof, see section 2 here. Can you please mention this in the docstring? It might even be a "Good First Project"!
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…ined Lipschitz functions (#11530) Any Lipschitz function on a subset of a metric space, into a finite-dimensional real vector space, can be extended to a globally defined Lipschitz function (up to worsening slightly the Lipschitz constant).
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Any Lipschitz function on a subset of a metric space, into a finite-dimensional real vector space, can be extended to a globally defined Lipschitz function (up to worsening slightly the Lipschitz constant).