Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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The term “rectifiable” for Jordan measurable sets is unrelated to rectifiable curves
Remarks
Some multivariable-analysis texts, including Munkres, call a bounded set rectifiable when its boundary has content zero. By A bounded set in is Jordan measurable iff its boundary is null, equivalently of content zero, these are exactly the bounded Jordan measurable sets of Jordan inner and outer content and Jordan measurable bounded sets in .
This terminology is unrelated to rectifiable curves and does not assert finite curve length. It creates no dependency on arc length.
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22 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- J. Munkres, Analysis on Manifolds, Jordan content terminology (standard reference, not scraped)