Integration and Measure
Course guide
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| Units | Suggested Learning Time | Basic Learning Materials and Readings | Exercises and projects | Evaluation Tests |
| Unit 1.1.
Measurable spaces |
10 hours |
1.1. Measurable spaces (PDF). |
EP 1.1. Measurable spaces (PDF). EP 1.1.1. Solutions (PDF). |
|
| Unit 1.2.
Measure spaces |
10 hours |
1.2. Measure spaces (PDF). |
EP 1.2. Measure spaces (PDF). EP 1.2.1. Solutions (PDF). |
|
| Unit 1.3.
Construction of measures |
10 hours |
EP 1.3. Construction of measures (PDF). EP 1.3.1. Solutions (PDF). |
||
| Unit 2.1.
Integration of positive functions |
10 hours |
EP 2.1. Integration of positive functions (PDF). EP 2.1.1. Solutions (PDF). |
||
| Unit 2.2.
Integration of general functions |
10 hours |
EP 2.2. Integration of general functions (PDF). EP 2.2.1. Solutions (PDF). |
EV 1. Intermediate Control 1 (PDF). EV 1.1. Solution (PDF). |
|
| Unit 2.3.
Integration on product spaces |
10 hours |
EP 2.3. Integration on product spaces (PDF). EP 2.3.1. Solutions (PDF). |
EV 2. Intermediate Control 2 (PDF). EV 2.1. Solution (PDF). |
|
| Unit 2.4.
Decomposition of measures |
10 hours |
EP 2.4. Decomposition of measures (PDF). EP 2.4.1. Solutions (PDF). |
||
| Unit 2.5.
Lp spaces |
10 hours |
2.5. Lp spaces (PDF). |
EP 2.5. Lp spaces (PDF). EP 2.5.1. Solutions (PDF). |
|
| Unit 3.1.
Integrals depending |
10 hours |
EP 3.1. Integrals depending on a parameter (PDF). EP 3.1.1. Solutions (PDF). |
EV 3. Evaluation test 1 (PDF). EV 3.1. Solution (PDF). |
|
| Unit 3.2.
Fourier transform |
10 hours |
3.2. Fourier transform (PDF). |
EP 3.2. Fourier transform (PDF). EP 3.2.1. Solutions (PDF). |
EV 4. Evaluation test 2 (PDF). EV 4.1. Solution (PDF). |
| Unit 3.3.
Laplace transform |
10 hours |
3.3. Laplace transform (PDF). |
EP 3.3. Laplace transform (PDF). EP 3.3.1. Solutions (PDF). |
EV 5. Evaluation test 3 (PDF). EV 5.1. Solution (PDF). |