  Prefix normal words are binary words that have no factor with more $1$s than
the prefix of the same length. Finite prefix normal words were introduced in
[Fici and Lipt\'ak, DLT 2011]. In this paper, we study infinite prefix normal
words and explore their relationship to some known classes of infinite binary
words. In particular, we establish a connection between prefix normal words and
Sturmian words, between prefix normal words and abelian complexity, and between
prefix normality and lexicographic order.
