How to use Statistical Learning theory in real analysis I begin the post trying to say that i don't know if this post is in compliance to community rules, so pardon me for any abuse.

I studied back at the university statistical learning theory. I studied PAC learning, VC Dimension, Uniform convergence etc etc. Recently i watched this talk with Vapnik https://www.youtube.com/watch?v=STFcvzoxVw4&amp;t=1346s in which he claims that deep learning is essentially a "bla bla interpretation" and also claims that 'every problem can be solved with statistical learning theory'.

I'm very confused about this. I can't see how I can apply statistical learning theory on real problems. 
Let's suppose I'm facing a new dataset with a clear task of binary classification, with many features and lots of training data. How am I supposed to check for example, if a hypothesis class H is PAC learnable, or in other words if it has a finite VC dimension? Don't take my example too literally, I just want to know if someone can point me out to an article,blog or some kind of answer that clearly shows how we can use this theorems and results in a real analysis.

Thank u
the development of the basic calculus , necessary for both formulating problems and numerical techniques for finding the minimum of a function
the theoretical development of theory of learning, such as the VC theory, in the same way it is used in statistics to do things like prove the central limit theorem