Uniform Convergence 一致收敛
Uniform convergence makes the approximation error small simultaneously at every point of a fixed domain.
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Uniform Integrability
Uniform integrability controls the contribution of large values across a family of random variables. It supplies the extra condition that upgrades convergence in probability to convergence in mean.
unique ergodicity 唯一遍历性
A continuous map of a compact metric space is uniquely ergodic when it has exactly one invariant probability measure. Oxtoby's theorem connects this uniqueness to uniform convergence of continuous-observable time averages.
Universal Property 泛性质
A universal property specifies an object together with structural maps through unique compatible factorizations.
Universal Quantifier 全称量词
Universal quantification asserts that a formula holds for every element of a specified domain, with all other parameters fixed.
Vector Space 向量空间
A vector space is an abelian group with scalar multiplication by a field satisfying the distributive and associative laws.
Wavefront Set 波前集
The smooth wavefront set records where a distribution fails to be smooth and in which cotangent directions.
Weak Derivative 弱导数
A weak derivative is a locally integrable function representing differentiation through integration against smooth test functions.
Weak Solution of a PDE 弱解
A weak PDE solution satisfies a specified integral identity in an explicitly chosen function space.
Yoneda Lemma 米田引理
The Yoneda lemma identifies transformations from a representable presheaf with one element of the target presheaf.