Exercise 1.2. If A,B ⊂ R,m∗(A) = 0, then m∗(A ∪B) = m∗(B) Proof: m∗(A ∪B) ≤ m∗(A) +m∗(B), and m∗(B) ≤ m∗(A ∪B), hence we have m∗(B) ≤ m∗(A ∪B) ≤ m∗(A) +m∗(B) = m∗(B) ∴ m∗(A ∪B) = m∗(B) Exercise 1.3. Prove E ∈M iff ∀ > 0,∃O ⊂ R open, such that E ⊂ O and m∗(O\E) < Proof: (⇒) O\E = E ∩O implies that m∗(O\E) = m∗(Ec ∩O), but we have m∗(O) = m∗(Ec ∩O) +m∗(E ∩O) So suppose m∗(E) < ∞ ⇒ m∗(Ec ∩ O) = m∗...

For the first time, the L-proline-catalyzed direct asymmetric self-aldolization of acetaldehyde is described affording (+)-(5S)-hydroxy-(2E)-hexenal 2 with ee's ranging from 57 to 90%. Further transformations of 2 into synthetically valuable building blocks are presented. A mechanism for the formation of 2 is proposed.

I.1 Two short problems: 1. Suppose that (X,A, μ) is a measure space, and X = ∪j=1Xj with Xj ⊂ Xj+1 for all j. Let χj be the indicator (characteristic) function of Xj, and let Mj denote the multiplication operator by χj acting on Z = Lp(X, dμ), 1 ≤ p < ∞. Show that Mj → I, the identity operator, in the strong operator topology, i.e. the weakest topology on bounded linear operators L(Z) in which ...

We describe a roundness classiication procedure , that is, a procedure to determine if the roundness of a planar object I is within some 0 from an ideal circle. The procedure consists of a probing strategy and an evaluation algorithm working in a feedback loop. This approach of combining probing with evaluation is new in computational metrology. For several deenitions of roundness, our procedur...

Using the means-end framework as a theoretical foundation, this article conceptualizes, constructs, refines, and tests a multiple-item scale (E-S-QUAL) for measuring the service quality delivered by Web sites on which customers shop online. Two stages of empirical data collection revealed that two different scales were necessary for capturing electronic service quality. The basic E-S-QUAL scale...

The purpose of this study is to explore the applicability of the E‐S‐QUAL instrument in the context of libraries’ social media services. As libraries have increased their use of social media such as Facebook and Twitter to interact with users and share information, the evaluation of the services has been emphasized to improve service strategies and meet user needs. However, there are no criteri...