The problem involves finding a subset A of the interval [0,1] that satisfies the condition A=cl(int A), where cl denotes closure and int denotes interior. Additionally, the boundary of A is required to not have measure zero.
The discussion is ongoing, with participants exploring various modifications to the fat Cantor set. Some guidance has been offered regarding the use of open intervals and the boundary of the closure of a set, but there is no explicit consensus on the correct approach yet.
Participants are grappling with the definitions of closure, interior, and boundary in the context of measure theory, and there is an acknowledgment of the complexity involved in modifying known sets to meet the problem's requirements.