  A measure without local dimension is a measure such that local dimension does
not exist for any point in its support. In this paper, we construct such a
class of Moran measures and study their lower and upper local dimensions. We
show that the related "free energy" function ($L^q$-spectrum) does not exist.
Nevertheless, we can obtain the full Hausdroff and packing dimension spectra
for level sets defined by lower and upper local dimensions. They can be viewed
as a generalized multifractal formalism.
