  We prove two results on the universality of polar codes for source coding and
channel communication. First, we show that for any polar code built for a
source $P_{X,Z}$ there exists a slightly modified polar code - having the same
rate, the same encoding and decoding complexity and the same error rate - that
is universal for every source $P_{X,Y}$ when using successive cancellation
decoding, at least when the channel $P_{Y|X}$ is more capable than $P_{Z|X}$
and $P_X$ is such that it maximizes $I(X;Y) - I(X;Z)$ for the given channels
$P_{Y|X}$ and $P_{Z|X}$. This result extends to channel coding for discrete
memoryless channels. Second, we prove that polar codes using successive
cancellation decoding are universal for less noisy discrete memoryless
channels.
