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.[1]

Properties of the trivial measure

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.


  1. ^ Porter, Christopher P. (2015-04-01). "Trivial Measures are not so Trivial". Theory of Computing Systems. 56 (3): 487–512. arXiv:1503.06332. doi:10.1007/s00224-015-9614-8. ISSN 1433-0490.