I am trying to understand the basic definition of realizable PAC learning from Shai Shalev-Shwartz's "understanding machine learning". They define a hypothesis class H to be PAC learnable if for every distribution D over the instances, and for any labeling function f, an approximately correct hypothesis can be learned with high probability over the random choice of a training set.
An issue that is not entirely clear ot me: they define PAC learnability as a property of an hypothesis class, i.e., of a solution. Intuitively I'd expect that learnability would be a property of the problem, as some problems are harder than others. What role do the properties of the problem play in the definition?