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# Integration Theory, part 1:

Below TS refers to the lecture notes: INTEGRATION THEORY by Tomas Sjödin.

The expected time for handing in the assignments is indicated below, but this is mainly to follow the pace of the course, and can be negotiated if needed. Note that all exercises from sections 4-7 of TS should be solved to pass the course (for undergraduate students aiming at a lower grade we can discuss suitable alternatives).

The below schedule is preliminary, and may be changed during the course if necessary.

Lecture 1: Some notation, motivation. Algebras and vector lattices (section 1-4 of TS).

Lecture 2: Review of algebras and lattices. Basic measure theory (section 4-5 of TS).

Homework assignments from section 4 handed in.

Lecture 3: Measure theory continues. (Section 5 of TS).

Lecture 4: Integration theory (Section 6 of TS).

Homework assignments from section 5 handed in.

Lecture 5: Integration theory continued (Section 6-7 of TS).

# Integration Theory, part 2:

The expected time for handing in the assignments is indicated below, but this is mainly to follow the pace of the course, and can be negotiated if needed. Note that all exercises from sections 8-13 of TS should be solved to pass the course (for undergraduate students aiming at a lower grade we can discuss suitable alternatives).

Lecture 6: Two theorems of Stone. Different Types of convergence. (Sections 8-9 of TS)

Homework assignments from section 6-7 handed in.

Lecture 7: Product Measures. Fubini's theorem (section 10 of TS).

Homework assignments from section 8-9 handed in.

Lecture 8: Signed measures and differentiation. (section 11 of TS).

Lecture 9: Signed measures and differentiation continued. L^p-spaces. (section 11-12 of TS).

Homework assignments from section 10 handed in.

Lecture 10: L^p-spaces continued. Continuous functionals on C(X). (section 12-13 of TS).

Sidansvarig: tomas.sjodin@liu.se