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High Quality Content by WIKIPEDIA articles! In mathematics, a filtration is an indexed set Si of subobjects of a given algebraic structure S, with the index i running over some index set I that is a totally ordered set, subject to the condition that if i j in I then Si Sj. The concept dual to a filtration is called a cofiltration.Filtrations are widely used in abstract algebra, homological algebra (where they are related in an important way to spectral sequences), and in measure theory and probability theory for nested sequences of -algebras. In functional analysis and numerical analysis, other terminology is usually used, such as scale of spaces or nested spaces.