Independence and atoms
Gábor J. Székely, Tamás F. Móri · Proceedings of the American Mathematical Society · 2001
We prove that if the range of a probability measure P P contains an interval [ 0 , ε ] [0,\varepsilon ] , ε > 0 \varepsilon >0 , then there are infinitely many (nontrivial) independent events in this probability space.