The vague topology is the weak-* topology on C0(X)*. The corresponding topology on M(X) induced by the isometry from C0(X)* is also called the vague topology on M(X). Thus, in particular, one may refer to vague convergence of measure μn → μ.
One application of this is to probability theory: for example, the central limit theorem is essentially a statement that if μn are the probability measures for certain sums of independent random variables, then μn converge weakly to a normal distribution, i.e. the measure μn is "approximately normal" for large n.
Famous quotes containing the word vague:
“I well recall my horror when I heard for the first time, of a journalist who had laid in a pair of what were then called bicycle pants and taken to golf; it was as if I had encountered a studhorse with his hair done up in frizzes, and pink bowknots peeking out of them. It seemed, in some vague way, ignominious, and even a bit indelicate.”
—H.L. (Henry Lewis)