antisigma

Antisigma is not a standard, widely defined term in mainstream mathematics or related fields. In discussions where it appears, it is often presented as a proposed dual or opposite of a sigma-algebra, but there is no single universally accepted definition or formal object that carries this name.

One informal way the term has been contemplated is to define an antisigma-algebra as a family of subsets of a set X that is closed under complements and under countable intersections. By De Morgan’s laws, a family closed under complements and countable intersections is also closed under countable unions, and it would contain the universal set and the empty set. In that sense, such a structure would coincide with a sigma-algebra, making the “antisigma” label redundant for standard measure-theory purposes. Because of this redundancy, the term has not established itself as a distinct mathematical object in formal literature.

Outside of measure theory, “antisigma” may occasionally appear in informal or speculative contexts to indicate a dual notion, opposition to sigma notation, or a linguistic contrast rather than a rigorously defined concept. However, these usages are not standardized and vary by author.

In practice, when precision is required, the established concept to refer to is the sigma-algebra, with any discussion of an “antisigma” regarded as nonstandard or metaphorical. See also sigma-algebra, De Morgan’s laws, and lattice or order-theoretic dualities.