 The second objection is that even if ergodicity obtains, this is not sufficient to give us what we need. As we have seen above, ergodicity comes with the qualification ‘almost everywhere’. This qualification is usually understood as suggesting that sets of measure zero can be ignored without detriment. The idea is that points falling in a set of measure zero are ‘sparse’ and can therefore be neglected. The question of whether or not this move is legitimate is known as the ‘measure zero problem’.