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A multiresolution analysis of the [[Lp space|Lebesgue space]] <math>L^2(\mathbb{R})</math> consists of a [[sequence]] of nested [[linear subspace|subspaces]]
::<math>\{0\}\subset \dots\subset V_1\subset V_0\subset V_{-1}\subset\dots\subset V_{-n}\subset V_{-(n+1)}\subset\dots\subset L^2(\R)</math>
that satisfies certain [[self-similarity]] relations in time-space and scale-frequency, as well as [[Complete metric space|completeness]] and regularity relations.
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