MAT1501: lecture notes errata

Week 1 notes

I believe that all mistakes that have been pointed out to me have now been fixed. For reference, some mistakes that were present in the first version of the notes were:

one $\cup$ should be $\cap$ in line 4 of the proof of Theorem 2.

The "definition" of Hausdorff dimension as "the supremum of s greater than or equal to 0 such that the Hausdorff measure of A is infinite" is wrong if A has Hausdorff dimension 0 and finite H^0 measure. The other definition, involving infimums, is always correct however.

remark preceding statement of Theorem 3 in fact applies only to Borel sets, not arbitrary sets.

Lemma 6 should say that \mu is a Borel measure and E is a Borel set.

At some point in the proof of Theorem 5 I wrote (1/2) \epsilon^{-i} when I should have typed \epsilon 2^{-(i+1)}

Concerning Remark 3, the notion of a convex hull is not defined in an arbitrary metric space. The remark holds if X is R^n with the Euclidean metric, which is the most important special case