>>673
>The Division Paradox　は矛盾ではないって

下記は、あなたが紹介したんだっけ？ ありがとう 面白いね、時枝より
LMは、the assertion that all sets of reals are Lebesgue measurable か
ZF + DC + PB もか

>>677
>コルモゴロフの0-1法則
>Rの部分集合AはQ不変かつルベーグ可測なら、μ(A)=0またはμ(A)=1

弥勒菩薩さま、さすが
下記”Zero-One Law For R/Q (ZF)”ですね

https://stanwagon.com/
Stan Wagon, Prof. of Mathematics and Computer Science, Macalester College
https://stanwagon.com/public/TheDivisionParadoxTaylorWagon.pdf
A Paradox Arising from the Elimination of a Paradox Alan D. Taylor and Stan Wagon
P1
Abstract. We present a result of Mycielski and Sierpiński—remarkable and under-appreciated in our view—showing that the natural way of eliminating the Banach–Tarski Paradox by assuming all sets of reals to be Lebesgue measurableleads to another paradox about division of sets that is just as unsettling as the paradox being eliminated. The DivisionParadox asserts that the reals can be divided into nonempty classes so that there are more classes than there are reals.

P2
Zero-One Law For R/Q (ZF). Let A⊆R be Q-invariant. If A has the Baire property, then A is either meager or comeager. If A is measurable, then either (a) A intersects all bounded intervals in measure zero; or (b) A intersects all bounded intervals J in measure λ(J); if λ is countably additive, then either A or R＼A has measure zero. If λ is restricted to [0,1], then any set that is Q-invariant (modulo 1) has measure 0 or 1.

P3
We use LM for the assertion that all sets of reals are Lebesgue measurable. The theory ZF + DC + LM is consistent, pro-vided one assumes the consistency of the existence of an inaccessible cardinal.

Similarly, we use PB for the assertion that all sets of reals have the property of Baire. The theory ZF + DC + PB is equiconsistent with ZF[24]