Let f be a continuous real-valued function on R3. Suppose that for every sphere S of radius 1, the integral of f(x, y, z) over the surface of S equals 0. Must f(x, y, z) = 0 for all points (x, y, z)?

  • Liberalism [he/him,they/them]
    hexagon
    ·
    4 years ago

    A single circle can change as the sphere moves even if the integral over the whole thing doesn't, though.

    If it helps, the final answer is no, f doesn't have to be 0.