China allocated about a third of its $580bn recovery plan to green measures, concentrating on energy efficiency.
We present two methods for constructing consistent approximations to Dirac delta measures concentrated on piecewise smooth curves or surfaces.
Investments include £30m to be spent over three years on a Green Investment Package of energy efficiency measures, concentrating on domestic property.
We establish a general superposition principle for curves of measures solving a continuity equation on metric spaces without any smooth structure nor underlying measure, representing them as marginals of measures concentrated on the solutions of the associated ODE defined by some algebra of observables.
Assume that a signed measure of subsets of is such that the total variation measure is a discrete measure concentrated in a three-point set and (2.15).
If we take m = x ∗ δ t , where δ t is the Dirac measure concentrated in t, then m ∈ M ( [ 0, a 0 ], E ∗ ) and from (12) it follows that 〈 x ∗, u n ( t ) − u ( t ) 〉 → 0 as n → ∞.
Theorem 2.2 Suppose that μ is a nonnegative Radon measure concentrated on a Borel set E of zero p-capacity, and that g n is a bounded sequence of nonnegative L 1 functions which converges to μ in the narrow topology of measures.
We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd.
That is, its characteristic function takes the form {mathbb {E}}bigl(e^{i u J_{t}}bigr)= t int_{0}^{infty}bigl(e^{iuz}-1bigr) nu dz), (2.1) where ν is the Lévy measure concentrated on ((0,infty)) satisfying int_{0}^{infty}(zwedge1) nu dz) < infty.
If v n is a subsequence such that | v n | p ⋆ d x ⇀ ν for some measure ν, then there exist x i ∈ R N and ν i > 0, i = 1, 2, 3, … , such that ∑ i = 1 ∞ ν i p p ⋆ < ∞ and v n p ⋆ ⇀ | v | p ⋆ + ∑ i = 1 ∞ ν i δ x i = ν, where δ x i denotes the Dirac measure concentrated at x i.
