Quantum mechanics

Pure mathematics

Mathematical physics

Discrete mathematics

σ-finite measure

Data mining

Computer science

Discrete measure

Physics

Database

Mathematics

Borel measure

Invariant (physics)

Measure (data warehouse)

Combinatorics

Dynamical systems theory

Conjecture

Invariant measure

Probability measure

Ergodic theory

Advances in Mathematics

In this paper, the notion of measure complexity is introduced for a topological dynamical system and it is shown that Sarnak's Möbius disjointness conjecture holds for any system for which every invariant Borel probability measure has sub-polynomial measure complexity. We then apply this result to a number of situations, including certain systems whose invariant measure don't all have discrete spectrum.

Measure complexity and Möbius disjointness