Claim: To properly define a measure, one needs sigma algebra which are a special case of a topology as conservative systems are those systems that do not shrink their phase space over time.
Evidence: This problem was resolved by defining measure only on a sub-collection of all subsets; the so-called measurable subsets, which are required to form a σ-algebra. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity.