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Banach and Tarski: decomposition of point sets into congruent parts

Contribution grade

Logic, foundations and set theory · METHOD

Reference score230,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Proved finite equidecomposition of bounded subsets with interior in dimensions at least three.

Scientific scope

The record is the exact two-author 1924 French paper. It concerns nonmeasurable set-theoretic pieces, not a physically executable cutting process, and does not absorb Hausdorff’s antecedent or later refinements concerning choice principles and piece counts.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is the exact two-author 1924 French paper. It concerns nonmeasurable set-theoretic pieces, not a physically executable cutting process, and does not absorb Hausdorff’s antecedent or later refinements concerning choice principles and piece counts.

Contributors

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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