---
tag: VF057ASFT6
kind: statement
role: proposition
name: Weiss's conjecture
sources:
  - wikipedia: en:71038072@r1351515966
    locator: Hyperfinite equivalence relation, section Open problems > Weiss's conjecture
    note: adopted
    mention: wikipedia://en/71038072#P1KG
    sections: [Statement]
inventory: [VZSE7BQTTJ]
---

## Statement

The above examples seem to indicate that Borel actions of "tame" countable groups induce hyperfinite equivalence relations. Weiss conjectured that any Borel action of a countable amenable group on a standard Borel space induces a hyperfinite orbit equivalence relation. While this is still an open problem, some partial results are known.