The strong law implies the weak law (although there seem to be variations on exactly what hypothesis are assumed for the strong law vs the weak law which probably make this not true depending on your definition of the strong law and weak law). The weak law states convergence in probability whereas the strong law states convergence almost surely.
Why does the strong law imply the weak law? In real analysis convergence in measure and convergence almost everywhere don't imply each other. Can someone explain what are the subtle meanings behind the difference convergences and what they mean for the law of large numbers.