mistake in proof of theorem 1, section 2.1

[nasmith]

The "1" in the expressions for the probability that either classifier (f^BO or g) makes an error on x should actually be \sum_{y} \mathcal{D}(x, y) ... i.e., the marginal probability of x. As written, you're counting the probability of some x' that isn't equal to x being generated by the data-generating distribution as an error, for either classifier.