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Yemon Choi
Yemon Choi
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I am looking for the original author and the date of publication of the following result.

Theorem There exist subsets $E_i\subset [0,1)$, $i\in {\bf Z}$, pairwise disjoints and real numbers $a_i$ such that $$ [0,1) = \coprod_{i\in Z} E_i, \quad [0,2) = \coprod_{i\in {\bf Z}} a_i + E_i. $$$$ [0,1) = \coprod_{i\in {\bf Z}} E_i, \quad [0,2) = \coprod_{i\in {\bf Z}} a_i + E_i. $$ I am pretty sure that this is either Borel or Lebesgue. I remember having seen the result in the collected works of one of these two mathematicians, who advertised it as a reason to reject the axiom of choice.

I am looking for the original author and the date of publication of the following result.

Theorem There exist subsets $E_i\subset [0,1)$, $i\in {\bf Z}$, pairwise disjoints and real numbers $a_i$ such that $$ [0,1) = \coprod_{i\in Z} E_i, \quad [0,2) = \coprod_{i\in {\bf Z}} a_i + E_i. $$ I am pretty sure that this is either Borel or Lebesgue. I remember having seen the result in the collected works of one of these two mathematicians, who advertised it as a reason to reject the axiom of choice.

I am looking for the original author and the date of publication of the following result.

Theorem There exist subsets $E_i\subset [0,1)$, $i\in {\bf Z}$, pairwise disjoints and real numbers $a_i$ such that $$ [0,1) = \coprod_{i\in {\bf Z}} E_i, \quad [0,2) = \coprod_{i\in {\bf Z}} a_i + E_i. $$ I am pretty sure that this is either Borel or Lebesgue. I remember having seen the result in the collected works of one of these two mathematicians, who advertised it as a reason to reject the axiom of choice.

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coudy
coudy
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author of a paradoxical decomposition of the interval

I am looking for the original author and the date of publication of the following result.

Theorem There exist subsets $E_i\subset [0,1)$, $i\in {\bf Z}$, pairwise disjoints and real numbers $a_i$ such that $$ [0,1) = \coprod_{i\in Z} E_i, \quad [0,2) = \coprod_{i\in {\bf Z}} a_i + E_i. $$ I am pretty sure that this is either Borel or Lebesgue. I remember having seen the result in the collected works of one of these two mathematicians, who advertised it as a reason to reject the axiom of choice.