Natural density and probability, constructively

TL;DR

This paper provides a constructive framework for the frequentist interpretation of probability using natural density, introduces probabilistic versions of the Limited Principle of Omniscience, and proposes a pointfree, abstract definition of probability structures.

Contribution

It offers a novel constructive approach to probability via natural density, extending classical principles and defining an abstract, pointfree probability framework.

Findings

Constructive account of frequentist probability using natural density

Probabilistic versions of the Limited Principle of Omniscience introduced

Proposes a pointfree, abstract probability structure

Abstract

We give here a constructive account of the frequentist approach to probability, by means of natural density. Using this notion of natural density, we introduce some probabilistic versions of the Limited Principle of Omniscience. Finally we give an attempt general definition of probability structure which is pointfree and takes into account abstractely the process of probability assignment.