In mathematics, given two measurable spaces and measures on them, one can obtain a product measurable space and a product measure on that space. Conceptually, this is similar to defining the Cartesian product of sets and the product topology of two topological spaces, except that there can be many natural choices for the product measure. A product measure (also denoted by by many authors)is defined to be a measure on the measurable space satisfying the property for all . (In multiplying measures, some of which are infinite, we define the product to be zero if any factor is zero.)