Elements of Real Analysis II – Take-Home Final代写代考

第一部分

LEBESGUE INTEGRATION FOR FUNCTIONS OF A SINGLE REAL VARIABLE

第二部分

ABSTRACT SPACES: METRIC, TOPOLOGICAL, BANACH, AND HILBERT SPACES

虽然期末考试量不多，但是做题还是挺煎熬的，尤其是对于第一次研修这门的童鞋来讲！

III Measure and Integration: General Theory 335
17 General Measure Spaces: Their Properties and Construction 337
17.1 Measures and Measurable Sets ……………………… 337
17.2 Signed Measures: The Hahn and Jordan Decompositions ……….. 342
17.3 The Carath6odory Measure Induced by an Outer Measure ……….. 346

22 Invariant Measures 477
22.1 Topological Groups: The General Linear Group ……………. 477
22.2 Kakutani’s Fixed Point Theorem ……………………. 480
22.3 Invariant Borel Measures on Compact Groups: von Neumann’s Theorem . . 485
22.4 Measure Preserving Transformations and Ergodicity: The Bogoliubov-Krilov
Theorem ………………………………… 488