Let $X$ be a non-empty set and $\mu:2^X\to[0,\infty]$ be a map. Do you happen to know good examples of such $\mu$s that do not satisfy either the monotonicity or countable subadditivity of a proper outer measure? My intuition is really tied to outer measures so I don't really know how to construct such examples. Thanks!
2026-03-26 11:04:12.1774523052
Example of a set mapping that is not an outer measure by violating either monotonicity or subadditivity
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