Approximately 2-local derivations on the finite von Neumann algebras

The paper deals with approximately 2-local derivations on the finite von Neumann algebra. The definition of approximately 2-local derivations is considered based on the definition of 2-local derivation. That is, we prove that every approximately 2-local derivation on the finite von Neumann algebra is a derivation by using the property of the linear Jordan derivation.