1. Exercise 3: “… cannot be replaced by any smaller quantity in general” – probably bigger rather than smaller.

2. Exercise 6, part 1 : “… more generally preserves $\chi’$-valued functions” – probably $\chi’$-measurable instead.

*[Corrected, thanks – T.]*

*[Removed – T.]*

Where the separability assumption were used in the first proof of Theorem 2?

*[The first proof is in fact valid for inseparable Hilbert spaces also. -T]*

[* To show , one can either use Jensen, or else apply Cauchy-Schwarz to the functions and . -T*]