 Such a sequence might represent an attempt to construct 'better and better' approximations to a desired measure μ that is difficult to obtain directly.The meaning of 'better and better' is subject to all the usual caveats for taking limits; for any error tolerance ε > 0 we require there be "N" sufficiently large for "n" ≥ "N" to ensure the 'difference' between μ"n" and μ is smaller than ε.Various notions of convergence specify precisely what the word 'difference' should mean in that description; these notions are not equivalent to one another, and vary in strength.