The method is based on a simple fact that remained unnoticed until now: Work on a quantum system can be measured by performing a generalized quantum measurement at a single time. We present a new method to measure the work w performed on a driven quantum system and to sample its probability distribution P (w ). Work Measurement as a Generalized Quantum Measurement Thus, the usual sorts of measurability properties used in connection with Hausdorff measure, for example measures of sections and projections, remain true for packing measure. On the other hand, we show that the packing dimension functions are measurable with respect to the -algebra generated by the analytic sets. Whereas the Hausdorff dimension function on the space of compact sets is Borel measurable, the packing dimension function is not. We do this by determining the descriptive set-theoretic complexity of the packing functions. In this paper, we find a basic limitation on this possibility. The question arises as to whether there is some simpler method for defining packing measure and dimension. This makes packing measure somewhat delicate to deal with. However, in contrast to Hausdorff measure, the usual definition of packing measure requires two limiting procedures, first the construction of a premeasure and then a second standard limiting process to obtain the measure. Packing measure is a sort of dual of Hausdorff measure in that it is defined in terms of packings rather than coverings. These notions are playing an increasingly prevalent role in various aspects of dynamics and measure theory. Measure and dimension functions: measurability and densitiesĭuring the past several years, new types of geometric measure and dimension have been introduced the packing measure and dimension, see, and. Thus, multilevel intervention research benefits from thoughtful theory-driven planning and design, an interdisciplinary approach, and mixed methods measurement and analysis. Furthermore, multilevel intervention research requires identification of key constructs and measures by level and consideration of interactions within and across levels. Measurement considerations that are associated with multilevel intervention research include those related to independence, reliability, validity, sample size, and power. Discussion Measurement issues may be especially complex when conducting multilevel intervention research. Discussion of the independence, validity, and reliability of measures was scant. Group-, organization-, and community-level measures were rarely used. Results The vast majority of measures used in multilevel cancer intervention studies were individual level measures. Additionally, literature from health services, social psychology, and organizational behavior was reviewed to identify measures that might be useful in multilevel intervention research. Ultimately, 234 multilevel articles, 40 involving cancer care interventions, were identified. Methods One-thousand seventy two cancer care articles from 2005 to 2010 were reviewed to examine the state of measurement in the multilevel intervention cancer care literature. However, taking a multilevel approach to cancer care interventions creates both measurement challenges and opportunities. Clauser, Steven B.īackground Multilevel intervention research holds the promise of more accurately representing real-life situations and, thus, with proper research design and measurement approaches, facilitating effective and efficient resolution of health-care system challenges. Multilevel Interventions: Measurement and MeasuresĬharns, Martin P. An application to Bohm's model of the Einstein-Podolsky-Rosen situation suggests that a faulty understanding of quantum measurements is at the root of this paradox. Quantum measurements are noncontextual in the original sense employed by Bell and Mermin: if =0 ,≠0, the outcome of an A measurement does not depend on whether it is measured with B or with C. Applications include Einstein's hemisphere and Wheeler's delayed choice paradoxes, and a method for analyzing weak measurements without recourse to weak values. The result supports the idea that equipment properly designed and calibrated reveals the properties it was designed to measure. A solution to the second measurement problem, determining what prior microscopic properties can be inferred from measurement outcomes ("pointer positions"), is worked out for projective and generalized (POVM) measurements, using consistent histories.
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