Multiresolution analysis plays a major role in wavelet theory. In this paper, multiresolution of Lp spaces is studied. Let S be a shift-invariant subspace of Lp(IR) (1 ≤ p ≤ ∞) generated by a finite number of functions with compact support, and let Sk be the 2-dilate of S for each integer k ∈ ZZ. It is shown that the intersection of Sk (k ∈ ZZ) is always trivial. It is more difficult to deal wi...