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 was able to believe for years that going to Madame Swann’s was a vague chimera that I would never attain; after having passed a quarter of an hour there, it was the time at which I did not know her which became to me a chimera and vague, as a possible destroyed by another possible.”
—Marcel Proust (1871–1922)