Apparently, the closest thing I've found would be normal number <http://mathworld.wolfram.com/NormalNumber.html> 


But requiring that every finite words occurs is weaker than this property. So I'm wondering if there are any study on this topic.


My original goal is to find a criterion for a Büchi automaton not to recognize some infinite word like this. There's been a post here [Proof that the $\omega$-language consisting of all words containing every finite word as a factor is not rational/regular](https://mathoverflow.net/questions/145375/proof-that-the-omega-language-consisting-of-all-words-containing-every-finite) , but there were no references to such a class of words.


Maybe all this is obvious to specialists, but I couldn't find anything with our universal friend google :)


Thank you!



Is there a name for infinite words containing every finite words?
One term that is used is [disjunctive sequence](http://en.wikipedia.org/wiki/Disjunctive_sequence). The linked article mentions some references, including an [overview](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.1370) (from 1997) by Calude, Priese, and Staiger.


