We derive Sobolev–Poincaré inequalities that estimate the Lq(d μ) norm of a function on a metric ball when μ is an arbitrary Borel measure. The estimate is in terms of the L1(d ν) norm on the ball of a vector field gradient of the function, where d ν dx is a power of a fractional maximal function of μ. We show that the estimates are sharp in several senses, and we derive isoperimetric inequalities as corollaries. 1991 Mathematics Subject Classification: 46E35, 42B25.