# Sum of Banach valued Borel measurable functions need not be Borel measurable?

Sum of Banach valued Borel measurable functions need not be Borel measurable when the Banach space is not separable. Any references to this result? Many thanks!

• Does the domain also have to be a topological space equipped with the Borel $\sigma$-algebra, or can it be any measurable space? – epimorphic May 29 '15 at 16:52