Against Cavalieri’s Principle? A Paradoxical Example in Dynamics

Author(s):

H. Rajabzadeh , A. Rastegar , M. Nassiri

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

There exists a continuous family of disjoint smooth curves, partitioning the unit square, such that one can choose only one point from each curve to construct a measurable set whose area is equal to 1. This contradicts our intuition which resembles Cavalieri’s principle and Fubini’s theorem! So, what is the problem? In this note, we discuss the theorem (due to A. Katok) and answer this question.

Keywords:

Cavalieri’s principle , Fubini’s Theorem , foliation , absolute continuity

Language:
Persian
Published:
Journal of Mathematical Culture and Thought, Volume:41 Issue: 2, 2023
Pages:
73 to 95
https://www.magiran.com/p2551893