Math 714 Final Review
The following should help prepare for the final exam
that will given on Monday, May 9 at noon-2pm in AB635.
The final covers chapters 4, 5 and sections 6.5-6.6 and 9.1-9.4.
The final does not cover Section 4.7.
Definitions
- Definitions 4.1, 4.2, 4.3.
- Definitions 4.15, 4.18, 4.22, 4.23, 4.24.
- Definitions 5.1, 5.3, 5.4, 5.5, 5.6, 5.8, 5.10, 5.11, 5.12.
- Definitions 6.9, 6.10, 6.11
- Definitions 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, 9.9.
Statements of Theorems
- Monotone Convergence Theorem (Theorem 4.6)
- Dominated Convergence (Theorem 4.9)
- Borel-Cantelli Lemma (Theorem 5.1)
- Holder's Inequality (Theorem 9.9)
- Radon-Nikodym Theorem (Theorem 6.10)
- Riesz Representation Theorem (Theorem 9.12)
Homework Problems
- All problems from assignments 1, 2, 4 and 5.
Proofs of Theorems
- Part (a) of Borel-Cantelli Lemma.
- Theorem 5.6, Proposition 5.8.
- The proofs of Proposition 9.4 and Theorem 9.6 presented in class.
- Theorem 9.9 and Theorem 9.10.
- Proof that L^1 is complete as in Theorem 9.11 with p = 1.
- Proof of uniqueness of the function f in the Theorem 6.10 as on page 369.
Surprise Problems
- The exam will include some simple surprise problems.
Last Updated:
Tue May 3 14:13:30 PDT 2011