Probability theory | Measures (measure theory)

Isotropic measure

In probability theory, an isotropic measure is any mathematical measure that is invariant under linear isometries. It is a standard simplification and assumption used in probability theory. Generally, it is used in the context of measure theory on -dimensional Euclidean space, for which it can be intuitive to study measures that are unchanged by rotations and translations. An obvious example of such a measure is the standard way of assigning a measure to subsets of n-dimensional Euclidean space: Lebesgue measure. (Wikipedia).

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Related pages

Lévy process | Random variable | Lebesgue measure | Probability density function | Absolute continuity | Probability theory | Measure (mathematics) | Isometry | Probability distribution | Euclidean space | Borel measure | Stochastic process | Subset