# A pointwise bipolar theorem

## TL;DR

This paper establishes a pointwise bipolar theorem for certain convex sets of measurable functions, extending duality results in optimal transport and financial hedging without tightness assumptions.

## Contribution

It introduces a novel pointwise bipolar theorem applicable to liminf-closed convex sets, broadening duality theory in measure and finance.

## Key findings

- Derived a transport duality for non-tight marginals
- Established a superhedging duality in discrete-time finance
- Extended duality results beyond tight measure assumptions

## Abstract

We provide a pointwise bipolar theorem for liminf-closed convex sets of positive Borel measurable functions on a sigma-compact metric space without the assumption that the polar is a tight set of measures. As applications we derive a version of the transport duality under non-tight marginals, and a superhedging duality for semistatic hedging in discrete time.