Trivial measure

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In mathematics, specifically in measure theory, the trivial measure on any measurable space (X, Σ) is the measure μ which assigns zero measure to every measurable set: μ(A) = 0 for all A in Σ.

Properties of the trivial measure[edit]

Let μ denote the trivial measure on some measurable space (X, Σ).

Suppose that X is a topological space and that Σ is the Borel σ-algebra on X.