Justifying typicality measures of Boltzmannian statistical mechanics and dynamical systems

• This paper is about justifying measures as typicality measures.
• Measures in statistical mechanics and dynamical systems theory are considered.
• I argue that Pitowsky's (2012) justification of typicality measures is problematic.
• I provide a new justification for interpreting measures as typicality measures.
• The main premises are invariance and that typicality relates to probabilities.

A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's (2012) justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. The main premises are that typicality measures are invariant and are related to the initial probability distribution of interest (which are translation-continuous or translation-close). The conclusions are two theorems which show that the standard measures of statistical mechanics and dynamical systems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilon-ergodic, there are uniqueness results about typicality measures.