Improvement of the Theorem on Local Ergodicity

We prove here that in the Theorem on Local Ergodicity for Semi-Dispersive Billiards (proved by N. I. Chernov and Ya. G. Sinai in 1987) the recently added condition (by P. B\'alint, N. Chernov, D. Sz\'asz, and I. P. T\'oth, in order to save this fundamental result) on the algebraic character of the smooth boundary components of the configuration space is unnecessary. Having saved the theorem in its original form by using additional ideas in the spirit of the initial proof, the result becomes stronger and it applies to a larger family of models.