- Bouligand dimension and almost Lipschitz embeddings,
Pacific J. Math. 202 (2002), no. 2, 459--474.
Theorem 3.2 on the Bouligand (or Assouad) dimension of the product of sets is wrong as stated. In fact there exists compact sets

*A*and*B*such thatdim _{b}(*A*x*B*) < dim_{b}(*A*) + dim_{b}(*B*),see Larman [Proc. London Math. Soc. (3) 17 (1967), 178--192].

The proof in the paper is correct when

*A*=*B*, in which casedim _{b}(*A*x*A*) = 2dim_{b}(*A*).Only this result is used in the remainder of the paper.

- Continuous Data Assimilation Using General Interpolant Observables, Journal of Nonlinear Science, 2013, pp. 1--27.
Lemma 1 misquoted the uniform Gronwall inequality from Jones and Titi [Lemma 4.1, Physica D (1992), 165--174]. The correct statement should be

**Lemma 1.**Let α be a locally integrable real valued function on (0,∞) satisfying for some 0 <*T*< ∞ the following conditions:*liminf*_{t→∞}∫_{t}^{t+T}α(*s*)d*s*= γ > 0and

*limsup*_{t→∞}∫_{t}^{t+T}max(−α(*s*),0)d*s*= Γ < ∞.Suppose

*Y*is an absolutely continuous non-negative function on (0,∞) such thatd *Y*/d*t*+ α*Y*≤ 0almost everywhere on (0,∞). Then

*Y*→ 0 as*t*→ ∞.Subsequent applications of the uniform Gronwall inequality in the paper are correct, except the words

*limsup*should read*liminf*. In particular, this error does not effect any results or proofs appearing in the paper.In the appendix the definition of ρ is missing a minus sign and for |ξ| < 1 should read

ρ(ξ) = K _{0}exp(−1/(1−|ξ|^{2}))