# Weak limit of abs. continuous measures

1. Sep 23, 2011

### tom85

say we have a sequence of probability measures on R, such that each one is abs. continuous wrt the Lebesgue measure...

is it possible that these measures converge weakly to a measure which is _not_ abs. continuous wrt the Lebesgue measure?

2. Sep 26, 2011

### bpet

yes, e.g. normal distribution as variance goes to zero.