Relation between feasibility of learning and Hoeffding's Inequality.

[jlaurentum]

Hello.

I understand that learning is picking out a function from a candidate set of functions that most closely resembles the target function. The feasibility of learning would be related to how close this resemblance is.

I understand also that Hoeffding's Inequality is an upper bound to the probability that the in-sample error rate deviates significantly from the real error rate. In the end, this upper bound simply implies that given a large enough sample, estimating the real error rate is feasible.

Is there any misconception in anything here so far?

So my question is: what does the Hoeffding inequality say about the feasibility of learning? Shouldn't it be feasibility of verifying hypothesis?