Several people have asked me for a more mathematically precise formulation of Thomas Piketty’s Second Fundamental Law of Capitalism, as well as a more careful statement of its proof and of the boundary conditions over which the proof applies, with some attention to the unusual and exceptional cases. I have written up some notes that are an attempt to comply with those requests. While I have attempted to be as precise as possible in laying out the proof, I have tried to avoid introducing any more rigor than is absolutely necessary for an informed reader to understand how the proof goes through. I have assumed a familiarity with reasoning about limits at the level of elementary calculus.
The notes can be downloaded here.