.

As potentially only has measure , and hence (which is contained in the inverse image under a projection of ) cannot have a larger measure.

*[Corrected, thanks – T.]*

Correct me if I am wrong, but is the second paragraph necessary: “It is also clear… closed under complements. ” As , the proof already shows is closed under complements, .

]]>Despite the failure of Tonelli’s theorem in the {\sigma}-finite setting…

Do you mean that Tonell fails in the non-sigma-finite setting instead?

*[Corrected, thanks – T.]*

*[No: see Theorem 36. -T]*

The line above Exercise 23 (Lebesgue-Stieltjes measure, pure point case)

should be

*[Corrected, thanks – T.]*

I guess you mean equation (3).

*[Corrected, thanks – T.]*

In the proof of Proposition 30 (Existence and uniqueness of product measure),

In the end of the line starting with “Now we show that”, it should be

In Corollary 40 (Tonelli’s theorem for sets), the RHS of last equality should be

In Exercise 44, the line below “such that”, the LHS and RHS of the inequality is the same. (One of them should be dxdy)

Same for the integrals after “respectively, and that” in the same exercise.

*[Corrected, thanks – T.]*

In the proof of Theorem 18 (Existence of Lebesgue-Stieltjes measure), did you forget to define -volume ?

*[Correction added, thanks – T.]*

*[Corrected, thanks – T.]*