  Let $W$ be a channel where the input alphabet is endowed with an Abelian
group operation, and let $(W_n)_{n\geq 0}$ be Ar{\i}kan's channel-valued
polarization process that is obtained from $W$ using this operation. We prove
that the process $(W_n)_{n\geq 0}$ converges almost surely to deterministic
homomorphism channels in the noisiness/weak-$\ast$ topology. This provides a
simple proof of multilevel polarization for a large family of channels,
containing among others, discrete memoryless channels (DMC), and channels with
continuous output alphabets. This also shows that any continuous channel
functional converges almost surely (even if the functional does not induce a
submartingale or a supermartingale).
