Lebesgue measure 勒贝格测度
Lebesgue measure on R^n is the complete measure obtained by restricting the countable rectangular-cover outer measure to the sets satisfying the Carathéodory splitting criterion.
Terminology & Translations
No matching entries. Clear filters or try another keyword.
Lebesgue outer measure 外测度
The Lebesgue outer measure of any E in R^n is the infimum of sums of rectangular volumes over all countable rectangle families covering E.
left module 左模
An abelian group with a distributive, associative unital left scalar action of a ring $R$.
left-continuous real function 左连续函数
A real function is left-continuous at a if its limit along domain points increasing to a equals f(a).
Levi–Civita connection Levi-Civita 联络
For a smooth Riemannian manifold, the unique connection on its tangent bundle that preserves the metric and has zero torsion: its covariant derivatives satisfy the metric product rule and their antisymmetric difference…
Li–Yorke chaos Li-Yorke混沌
A continuous map of a metric space is Li–Yorke chaotic when it admits an uncountable set in which every distinct pair satisfies $\liminf_n d(T^nx,T^ny)=0$ and $\limsup_n d(T^nx,T^ny)>0$.
Li–Yorke scrambled pair Li-Yorke攀援偶对
Distinct points $x,y$ in a metric dynamical system with $\liminf_n d(T^nx,T^ny)=0$ and $\limsup_n d(T^nx,T^ny)>0$.
Lie group 李群
A group equipped with a finite-dimensional Hausdorff, second countable smooth manifold structure without boundary for which multiplication and inversion are smooth maps.
limit inferior of a real sequence 数列下极限
The limit inferior of a real sequence a_n is the extended-real limit of the increasing tail infima inf_{k>=n} a_k.
limit of a real sequence 数列极限
A real sequence has limit a if, for every positive epsilon, all terms beyond some index lie within epsilon of a.
limit superior of a real sequence 数列上极限
The limit superior of a real sequence a_n is the extended-real limit of the decreasing tail suprema sup_{k>=n} a_k.
linear independence 线性无关
A family $(v_i)$ is linearly independent if every finite relation $\sum_i a_iv_i=0$ has all coefficients zero.
linear map 线性映射
A map $T:V\to W$ between vector spaces over the same field $F$ satisfying $T(av+bw)=aT(v)+bT(w)$.
linear representation of a finite group 有限群的线性表示
A homomorphism $\rho:G\to\operatorname{GL}(V)$ for a finite group $G$ and an $F$-vector space $V$.
Littlewood–Paley decomposition Littlewood-Paley分解
An inhomogeneous Littlewood–Paley decomposition splits a tempered distribution into smooth Fourier multiplier pieces using a low-frequency cutoff and dyadic annular cutoffs whose sum is one; the piece sum reconstructs…
localization of a commutative ring 交换环的局部化
For a multiplicative set $S$, the universal ring $S^{-1}R$ receiving a map from $R$ that makes every member of $S$ invertible.
locally compact space 局部紧致
A topological space in which every point lies in an open subset contained in some compact subspace; no Hausdorff condition is included in this definition.
locally connected space 局部连通
A space in which every open neighborhood of a point contains a connected open neighborhood of that point.
locally path connected space 局部道路连通
A space in which every open neighborhood of a point contains a path connected open neighborhood of that point.
locally small category 局部小范畴
A category whose collection of morphisms between each fixed pair of objects is a set.
logical consequence 语义蕴含
For a sentence set Γ, a sentence φ is a consequence when every structure satisfying Γ satisfies φ.
logical equivalence 逻辑等价
Two propositional formulas are logically equivalent when they have equal truth values under every valuation.
logical validity 逻辑有效
A sentence is logically valid if every nonempty structure for its language satisfies it.
Lp convergence of random variables p次平均收敛
For $p\ge1$, random variables $X_n,X$ on one probability space with finite $p$th moments converge in $L^p$ when $E|X_n-X|^p\to0$.
Lp space Lp空间
For a measure space and 1<=p<infinity, Lp consists of measurable real or complex functions with finite integral of |f|^p, identified when equal almost everywhere, with norm (integral |f|^p)^(1/p). L-infinity instead…