Title EPSilon-SIMULTANEOUS APPROXIMATIONS OF DOWNWARD SETS Type of Research Article Keywords "-simultaneous approximation, downward set, lattice Banach space. Abstract We prove some results on characterization of "-simultaneous approximations of downward sets in vector lattice Banach spaces. Also, we give some results about simultaneous approximations of normal sets. Researchers Hosein Alizadeh (First Researcher)، Shahram Rezapour (Second Researcher)، Seyyes Mansour Vaezpour (Third Researcher)