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Counterexample

Is this true?

A set of measure zero is countable

No — it is false.

The counterexample

The Cantor set

Why it fails

Uncountable, yet measure zero.

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Hypothesis dropped

A theorem applied without checking one of its preconditions.

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A set with no measure: the Vitali construction

measure

Go deeper· Explained in full in Lebesgue measure and measurable functions· Asked in CSIR NET June 2023· From Lebesgue Measure and Integration › Measurable sets and functions

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