We conceptualize and measure upward mobility over income or wealth. At the core of our exercise is the Growth Progressivity Axiom: transfers of instantaneous growth rates from relatively rich to poor individuals increases upward mobility. This axiom, along with mild auxiliary restrictions, identifies an "upward mobility kernel" with a single free parameter, in which mobility is linear in individual growth rates, with geometrically declining weights on baseline incomes. We extend this kernel to trajectories over intervals. The analysis delivers an upward mobility index that does not rely on panel data. That significantly expands our analytical scope to data-poor settings.