[see also: classic
Theorems 1 to 3 are classical results, due to Lebesgue.
Since most of the results presented are quite classical (the novelty lies in the arrangement, and some of the proofs are new), I have not attempted to document the source of every item.
The following theorem is clearly motivated by the classical LP-decomposition.
Our proofs make substantial use of classical topology of the plane.
[Note the difference between classic and classical: classic means “of acknowledged excellence'' or “remarkably typical'' ( a classic example); and classical means “well-established, not modern''.]