feat(measure_theory/measure/finite_measure_weak_convergence): Characterize weak convergence of finite measures in terms of integrals of bounded continuous real-valued functions. (#14578)
Weak convergence of measures was defined in terms of integrals of bounded continuous nnreal-valued functions. This PR shows the equivalence to the textbook condition in terms of integrals of bounded continuous real-valued functions.
Also the file `measure_theory/measure/finite_measure_weak_convergence.lean` is divided to sections with dosctrings for clarity.
Co-authored-by: kkytola <39528102+kkytola@users.noreply.github.com>
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>