Continuous Selections for Vector Measures
Dov Samet · Mathematics of Operations Research · 1987
A vector measure is a many to one map; it maps many measurable sets onto the same point. A selection for a vector measure is a function which assigns to each point in the range of the vector measure only one measurable set which is mapped onto the point. The existence of a continuous selection for nonatomic vector measures is proved where the distance in the σ-field is the measure (for a given scalar measure) of the symmetric difference. A stronger version of continuous selection exists for strictly convex ranges.