A flexible application of the Stone-Weierstrass Theorem in General and Application in Probability Theory

Abstract

When applying the classical Stone-Weierstrass common version in Probability Theory for example but in other fields also, some problems may arise if all points of the compact set are not separated. A solution may consist in going back to the proof and finding alternative versions. In this note, we did it and come back with two flexible versions which are easily used for the needs of Probability Theory.