## Abstract

The standard theory of probability is based on Kolmogorov's measure-theoretic axioms. A less known alternative is the game-theoretic approach to probability. The purpose of this chapter is to give an introduction to the current state of game-theoretic probability. The chapter begins by stating a simple game-theoretic strong law of large numbers. This motivates the introduction of a general discrete-time forecasting protocol and the definition of game-theoretic expectation and probability. The chapter discusses the axiom of continuity for sets of available gambles, and the Doob's argument, which is useful in measure-theoretic and game-theoretic probability. Some limit theorems of game-theoretic probability are also outlined in the chapter. The chapter discusses a different kind of classical results of probability, the zero-one laws, in particular, the Lévy's zero-one law. The last section gives references for further reading.

Original language | English (US) |
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Title of host publication | Introduction to Imprecise Probabilities |

Publisher | wiley |

Pages | 114-134 |

Number of pages | 21 |

ISBN (Electronic) | 9781118763117 |

ISBN (Print) | 9780470973813 |

DOIs | |

State | Published - Aug 29 2014 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Keywords

- Axiom of continuity
- Discrete-time forecasting protocol
- Doob's argument
- Game-theoretic probability
- Lévy's zero-one law
- Measure-theoretic probability
- Strong law of large numbers