Convergence in measure under Finite Additivity

Abstract

We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained.

References in corpus (2)

• Sure Wins, Separating Probabilities and the Representation of Linear Functionals
• Some implications of Lebesgue decomposition

Cited by in corpus (3)

• A Version of Komlós Theorem for Additive Set Functions
• The Theorem of Halmos and Savage under Finite Additivity
• Some implications of Lebesgue decomposition