  We show that definable Whitney jets of class $C^{m,\omega}$, where $m$ is a
nonnegative integer and $\omega$ is a modulus of continuity, are the
restrictions of definable $C^{m,\omega}$-functions; "definable" refers to an
arbitrary given o-minimal expansion of the real field. This is true in a
uniform way: any definable bounded family of Whitney jets of class
$C^{m,\omega}$ extends to a definable bounded family of
$C^{m,\omega}$-functions. We also discuss a uniform $C^m$-version and how the
extension depends on the modulus of continuity.
