I know it is true that every countable set has measure zero, but is the converse true. Is it true that every set of measure zero is countable?
2026-04-13 05:03:49.1776056629
Is every set of measure zero countable?
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No. The Cantor set is probably the easiest example of an uncountable null set.
Of course, there are many others. For instance, every Lebesgue measurable set is a union of a Borel set and a null set.