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March 8, 2026Open Access

Weak extension of the ham-sandwich theorem : some ratio not in half

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Authors

HKHidefumi Kawasaki

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Overview

The paper demonstrates an extension of the ham-sandwich theorem, indicating implications for measurable sets and optimization theory.

Key Points

  • This research aims to extend the ham-sandwich theorem under conditions not requiring a halving of measures.
  • Application of Borsuk's antipodal theorem
  • Use of measurable sets with positive Lebesgue measure
  • Introduction of a hyperplane for division
  • Successful extension of the ham-sandwich theorem to ratios not in half
  • Demonstrates new conditions for dividing measurable sets

Cite This Study

Hidefumi Kawasaki (2024) studied this question.

synapsesocial.com/papers/69acc58f32b0ef16a404fdb2https://doi.org/10.15017/7407612
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