Conull set

In measure theory, a conull set is a set whose complement is null, i.e., the measure of the complement is zero.[1] For example, the set of irrational numbers is a conull subset of the real line with Lebesgue measure.[2]

A property that is true of the elements of a conull set is said to be true almost everywhere.[3]


  1. Führ, Hartmut (2005), Abstract harmonic analysis of continuous wavelet transforms, Lecture Notes in Mathematics, 1863, Springer-Verlag, Berlin, p. 12, ISBN 3-540-24259-7, MR 2130226.
  2. A related but slightly more complex example is given by Führ, p. 143.
  3. Bezuglyi, Sergey (2000), "Groups of automorphisms of a measure space and weak equivalence of cocycles", Descriptive set theory and dynamical systems (Marseille-Luminy, 1996), London Math. Soc. Lecture Note Ser., 277, Cambridge Univ. Press, Cambridge, pp. 59–86, MR 1774424. See p. 62 for an example of this usage.

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