A “fat” Cantor set

Example · Graduate

Terms

Term	This example	Why
nowhere dense	✓	A fat Cantor set is nowhere dense, because it contains no interval.
meager set	✓	A fat Cantor set is meager, because it is nowhere dense, even though its measure is positive.
measure zero	✗	A fat Cantor set does not have measure zero, because the intervals removed in its construction are small enough that it keeps a positive length.

Distinctions using this example

• Types of set sparsity

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