Upper and Lower Bounds for Probabilities in the Conditional Borel–Cantelli Lemma

Abstract

We obtain an inequality connected with a conditional version of the generalized Borel–Cantelli lemma.

Keywords:

• Conditional Borel–Cantelli lemma
• Conditional independence
• Lower bound
• Upper bound

Mathematics Subject Classification:

• Primary 60F15

Acknowledgments

The author thanks Mr. Xie Yuquan for clarifying the points in his article through a private communication.