 Pushforward measure

In measure theory, a discipline within mathematics, a pushforward measure (also push forward, push-forward or image measure) is obtained by transferring ("pushing forward") a measure from one measurable space to another using a measurable function.Given measurable spaces formula_1 and formula_2, a measurable mapping formula_3 and a measure formula_4, the pushforward of formula_5 is defined to be the measure formula_6 given by

This definition applies "mutatis mutandis" for a signed or complex measure.