Bibliographical notes

Notes to Chapter 1 Rudiments of measure theory may be found in. Classics in this field are and; see also. A short but excellent account on convex functions may be found in, Chapter V, Section 8. A classical detailed treatment may be found in. The proof of the Steinhaus Theorem is taken from.

Notes to Chapter 2 There are many excellent monographs devoted to Functional Analysis, including. Missing proofs of the statements concerning locally compact spaces made in 2.3.25 may be found in and.

Notes to Chapter 3 Among the best references on Hilbert spaces are and. The proof of Jensen's inequality is taken from; different proofs may be found in and. Some exercises in 3.3 were taken from and. An excellent and well-written introductory book on martingales is; the proof of the Central Limit Theorem is taken from this book. Theorems 3.6.5 and 3.6.7 are taken from. A different proof of 3.6.7 may be found e.g. in.

Notes to Chapter 4 Formula (4.11) is taken from. Our treatment of the Itô integral is largely based on. For detailed information on matters discussed in 4.4.8 see e.g., and. To be more specific: for integrals with respect to square integrable martingales see e.g. Proposition 3.4 p. 67, Corollary 5.4 p. 78, Proposition 6.1. p. 79, Corollary 5.4, and pp. 279–282 in, or Chapter 3 in or Chapter 2 in. See also, etc.