query: Lipschitz transformation maps measure zero sets to measure zero sets.
positive_passages.docid: 26246
positive_passages.text: Why does a Lipschitz function $f:\mathbb{R}^d\to\mathbb{R}^d$ map measure zero sets to measure zero sets?
negative_passages.docid: 127631
negative_passages.text: On a conformal mapping
negative_passages.docid: 101319
negative_passages.text: Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes
negative_passages.docid: 141366
negative_passages.text: Absolutely continuity and Lipschitz-like continuity
negative_passages.docid: 94899
negative_passages.text: Graph of a continuous function has measure zero
negative_passages.docid: 84264
negative_passages.text: the space of lipschitz function is complete with respect to some norm
negative_passages.docid: 97841
negative_passages.text: General property regarding outer measure for a nested sequence of sets (measurable or not).
negative_passages.docid: 90540
negative_passages.text: What is wrong in this proof: That $\mathbb{R}$ has measure zero
negative_passages.docid: 20810
negative_passages.text: Boundary of Ball of radius R has zero measure
negative_passages.docid: 26369
negative_passages.text: Proving seemingly obvious equations with measure theory
negative_passages.docid: 53663
negative_passages.text: outer measure and measurable sets
negative_passages.docid: 83046
negative_passages.text: A linear map, continuous at zero, is bounded
negative_passages.docid: 129623
negative_passages.text: A shrinking map that is not a contraction no fixed point.
negative_passages.docid: 107160
negative_passages.text: Open Set and Measure Theory
negative_passages.docid: 78344
negative_passages.text: Nonconstant linear functional on a topological vector space is an open mapping
negative_passages.docid: 88602
negative_passages.text: Inner regularity of Lebesgue measurable sets
negative_passages.docid: 93389
negative_passages.text: Uncountable sets of Hausdorff dimension zero