Counterexample

Is this true?

A nowhere dense set has measure zero

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

86 counterexamples are free — including most of the ones Part C leans on hardest.

Keep practicing

Hypothesis dropped

A theorem applied without checking one of its preconditions.

See real exam options built on this mistake Drill statements like this

Watch it happen

A set with no measure: the Vitali construction

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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