When we say that a condition holds everywhere except on a set of measure zero, we can say that the condition holds almost everywhere.
I want to say that a condition holds everywhere except on a set that is nowhere dense (i.e. a set that does not contain an interval). What is the "almost everywhere" equivalent shorthand notation for saying this? "Approximately almost everywhere" is my own name for it, but I am wondering if a formal name exists.
Best Answer
It is common to say that a property holds "generically" if it holds except on a meager set. A meager set is a countable union of nowhere dense sets - because meager sets and sets of measure zero are both closed under countable unions, meager is a better analogue of measure zero than nowhere dense (for most purposes).