实变函数与泛函分析中的英文单词和短语

实变函数和泛函分析RealVariableFunctionandFunctionalAnalysis第一章预备知识Chapter1PreliminaryKnowledge集合的运算operationofsets对等的集合equipotentsets基数base可数集countableset不可数集uncountableset上限集合upperlimitset下限集合lowerlimitset实数域fieldofrealnumbers第二章点集的拓扑概念Chapter2TopologicalConceptsforSets距离空间distancespace开集openset闭集closedset康托集Cantorset覆盖cover有限覆盖finitecover可数覆盖countablecover等价equivalence第三章测度论Chapter3MeasureTheory勒贝格测度lebesguemeasureG形集合GsetF形集合Fset波雷尔集合Borelset外侧度exteriormeasure可数可加countableadditivity正则性regularity第四章可测函数Chapter4MeasurableFunctions可测函数measurablefunctions几乎处处收敛almosteverywhereconvergence一致收敛uniformconvergence依测度收敛convergencebymeasure勒贝格控制收敛定理Lebesguecontrolconvergencetheorem里斯定理RiesztheoremLusin定理LusintheoremEorou定理Eoroutheorem第五章积分理论Chapter5IntegrationTheory积分定理integraltheory莱维单调收敛定理Levimonotonyconvergencetheorem法图引理fatoulemma富比尼定理Fubinitheorem有界变差函数boundedvariationfunction绝对连续函数absolutelycontinuousfunction实变函数和泛函分析中的英文单词和短语第六章抽象空间论Chapter6TheoryofAbstractSpaces三角不等式triangleinequality度量空间metricspace范数norm赋范空间normedspace凸集convexitypL-空间p-normedintegralspaceL-空间-normedintegralspaceC-空间continuousspace紧集compactset完备集合completeset不动点fixedpoint拓扑空间topologicalspace向量空间vectorspace锥core第七章抽象空间之间的映射Chapter7MappingbetweenAbstractSpaces柯西序列Cauchysequence完备化空间completespace完备子空间completesub-space收敛序列convergentsequence稠密集合denseset连续变换continuoustransformation微分differential凸组合convexcombination凸泛函convexfunctional阵列array弱紧性weakcompactness弱连续性weakcontinuous弱收敛weakconvergence弱星收敛weak*convergence内积innerproduct内积空间innerproductspace内点innerpoint同构isomorphism雅可比矩阵Jacobimatrix正交投影orthogonalprojection正交补orthogonalcomplement算子operator最佳逼近bestapproximation投影projection可分空间separablespace支撑空间supportfunctional共鸣定理resonancetheorem开映射定理resonancetheorem闭图像定理closedgraphtheorem共轭空间与共轭算子conjugatespaceandconjugateoperator