1、实变函数和泛函分析中的英文单词和短语实变函数和泛函分析Real Variable Function and Functional Analysis第一章 预备知识Chapter 1 Preliminary Knowledge集合的运算operation of sets对等的集合equipotent sets基数base可数集countable set不可数集uncountable set上限集合upper limit set下限集合lower limit set实数域field of real numbers第二章 点集的拓扑概念Chapter 2 Topological Concepts f
2、or Sets距离空间distance space开集open set闭集closed set康托集Cantor set覆盖cover有限覆盖finite cover可数覆盖countable cover等价equivalence第三章 测度论Chapter 3 Measure Theory勒贝格测度lebesgue measure形集合 set形集合 set波雷尔集合Borel set外侧度exterior measure可数可加countable additivity正则性regularity第四章 可测函数Chapter 4 Measurable Functions可测函数measura
3、ble functions几乎处处收敛almost everywhere convergence一致收敛uniform convergence依测度收敛convergence by measure勒贝格控制收敛定理Lebesgue control convergence theorem里斯定理Riesz theoremLusin定理Lusin theoremEorou定理Eorou theorem第五章 积分理论Chapter 5 Integration Theory积分定理integral theory莱维单调收敛定理Levi monotony convergence theorem法图引理
4、fatou lemma富比尼定理Fubini theorem有界变差函数bounded variation function绝对连续函数absolutely continuous function第六章 抽象空间论Chapter 6 Theory of Abstract Spaces三角不等式triangle inequality度量空间metric space范数norm赋范空间normed space凸集convexity-空间p-normed integral space-空间-normed integral spaceC-空间continuous space紧集compact set完
5、备集合complete set不动点fixed point拓扑空间topological space向量空间vector space锥core第七章 抽象空间之间的映射Chapter 7 Mapping between Abstract Spaces柯西序列Cauchy sequence完备化空间complete space完备子空间complete sub-space收敛序列convergent sequence稠密集合dense set连续变换continuous transformation微分differential凸组合convex combination凸泛函convex func
6、tional阵列array弱紧性weak compactness弱连续性weak continuous弱收敛weak convergence弱星收敛weak * convergence内积inner product内积空间inner product space内点inner point同构isomorphism雅可比矩阵Jacobi matrix正交投影orthogonal projection正交补orthogonal complement算子operator最佳逼近best approximation投影projection可分空间separable space支撑空间support functional共鸣定理resonance theorem开映射定理resonance theorem闭图像定理closed graph theorem共轭空间与共轭算子conjugate space and conjugate operator
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