SWhat changed
Hausdorff extended small-scale covering measures to fractional powers and more general gauge functions, and constructed perfect sets with positive finite measure at prescribed scales under explicit assumptions.
Scientific scope
Hausdorff extended small-scale covering measures to fractional powers and more general gauge functions, and constructed perfect sets with positive finite measure at prescribed scales under explicit assumptions. The construction uses specified covers, limiting diameters and gauge functions to measure sets and define dimension. A gauge choice is part of the object. Dimension need not equal a finite nonzero measure at the critical exponent, and this is not a universal physical scaling law. Later generalized measure/dimension results remain separate.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Felix Hausdorff · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Felix Hausdorff, Dimension und äußeres Maß — original 1919 article, dated March 1918
- S. D. Chatterji, collected-edition Commentary on H 1919 a — original/later-scope distinction
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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