  The magnetic penetration depth $\lambda(0)$ in polycrystalline MgB$_{2}$ for
different boron isotopes ($^{10}$B/$^{11}$B) was investigated by transverse
field muon spin rotation. No boron isotope effect on the penetration depth
$\lambda(0)$ was found within experimental error: $\Delta\lambda(0)/\lambda(0)
= -0.8(8)%$, suggesting that MgB$_{2}$ is an adiabatic superconductor. This is
in contrast to the substantial oxygen isotope effect on $\lambda(0)$ observed
in cuprate high-temperature superconductors.
