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This is a follow-up to some of my comments to the OP and to the answer that @Conifold gave. A few days ago I purchased a copy of the book that I had mentioned, Measure and the Integral by Lebesgue (1966). I was correct that this book is where, many years ago (1980s, possibly even late 1970s), I had read about Lebesgue's fascination with this “paradox”. ...

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