Vector and Operator Valued Measures and Applications is a collection of papers presented at the Symposium on Vector and Operator Valued Measures and Applications held in Alta, Utah, on August 7-12, 1972. The symposium provided a forum for discussing vector and operator valued measures and their applications to various areas such as stochastic integration, electrical engineering, control theory, and scattering theory. Comprised of 37 chapters, this volume begins by presenting two remarks related to the result due to Kolmogorov: the first is a theorem holding for nonnegative definite functions from T X T to C (where T is an arbitrary index set), and the second applies to separable Hausdorff spaces T, continuous nonnegative definite functions ? from T X T to C, and separable Hilbert spaces H. The reader is then introduced to the extremal structure of the range of a controlled vector measure ? with values in a Hausdorff locally convex space X over the field of reals; how the theory of vector measures is connected with the theory of compact and weakly compact mappings on certain function spaces; and Daniell and Daniell-Bochner type integrals. Subsequent chapters focus on the disintegration of measures and lifting; products of spectral measures; and mean convergence of martingales of Pettis integrable functions. This book should be of considerable use to workers in the field of mathematics.

For readers of Being Mortal and Modern Death, an ICU and Palliative Care specialist offers a framework for a better way to exit life that will change our medical culture at the deepest level In medical school, no one teaches you how to let a patient die. Jessica Zitter became a doctor because she wanted to be a hero. She elected to specialize in critical care—to become an ICU physician—and imagined herself swooping in to rescue patients from the brink of death. But then during her first code she found herself cracking the ribs of a patient so old and frail it was unimaginable he would ever come back to life. She began to question her choice. Extreme Measures charts Zitter’s journey from wanting to be one kind of hero to becoming another—a doctor who prioritizes the patient’s values and preferences in an environment where the default choice is the extreme use of technology. In our current medical culture, the old and the ill are put on what she terms the End-of-Life Conveyor belt. They are intubated, catheterized, and even shelved away in care facilities to suffer their final days alone, confused, and often in pain. In her work Zitter has learned what patients fear more than death itself: the prospect of dying badly. She builds bridges between patients and caregivers, formulates plans to allay patients’ pain and anxiety, and enlists the support of loved ones so that life can end well, even beautifully. Filled with rich patient stories that make a compelling medical narrative, Extreme Measures enlarges the national conversation as it thoughtfully and compassionately examines an experience that defines being human.

This textbook offers an accessible introduction to translation surfaces. Building on modest prerequisites, the authors focus on the fundamentals behind big ideas in the field: ergodic properties of translation flows, counting problems for saddle connections, and associated renormalization techniques. Proofs that go beyond the introductory nature of the book are deftly omitted, allowing readers to develop essential tools and motivation before delving into the literature. Beginning with the fundamental example of the flat torus, the book goes on to establish the three equivalent definitions of translation surface. An introduction to the moduli space of translation surfaces follows, leading into a study of the dynamics and ergodic theory associated to a translation surface. Counting problems and group actions come to the fore in the latter chapters, giving a broad overview of progress in the 40 years since the ergodicity of the Teichmüller geodesic flow was proven. Exercises are included throughout, inviting readers to actively explore and extend the theory along the way. Translation Surfaces invites readers into this exciting area, providing an accessible entry point from the perspectives of dynamics, ergodicity, and measure theory. Suitable for a one- or two-semester graduate course, it assumes a background in complex analysis, measure theory, and manifolds, while some familiarity with Riemann surfaces and ergodic theory would be beneficial.

In this survey the authors endeavor to give a comprehensive examination of the theory of measures having values in Banach spaces. The interplay between topological and geometric properties of Banach spaces and the properties of measures having values in Banach spaces is the unifying theme. The first chapter deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. Chapter II concentrates on measurable vector valued functions and the Bochner integral. Chapter III begins the study of the interplay among the Radon-Nikodym theorem for vector measures, operators on $L_1$ and topological properties of Banach spaces. A variety of applications is given in the next chapter. Chapter V deals with martingales of Bochner integrable functions and their relation to dentable subsets of Banach spaces. Chapter VI is devoted to a measure-theoretic study of weakly compact absolutely summing and nuclear operators on spaces of continuous functions. In Chapter VII a detailed study of the geometry of Banach spaces with the Radon-Nikodym property is given. The next chapter deals with the use of Radon-Nikodym theorems in the study of tensor products of Banach spaces. The last chapter concludes the survey with a discussion of the Liapounoff convexity theorem and other geometric properties of the range of a vector measure. Accompanying each chapter is an extensive survey of the literature and open problems.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1970.

Dr. Eric Najarian. He's young, talented, and ambitious. He has all the qualities they're looking for at White Memorial Hospital. He doesn't know he's being watched. Judged. An elite clique of medical professionals thinks he has what it takes to join their secret club. All the young doctor has to do is agree to play by their rules. But Eric has already seen too much. A missing corpse. An unspeakable mutilation. A brutal abduction. It's only the beginning of a plot of terrifying evil. A sinister plan the group will stop at nothing to hide. And if Eric refuses to become their colleague--he will be their next victim.

Master the world's fastest drawing program! Learn the principles of vector drawing as you learn technique, composition, and other art essentials--then apply your skills to creating websites, animations, logos, photographic retouches, and more. Xara Xtreme 5: The Official Guide shows you how to customize the software, use QuickShapes, draw vector paths, use fills for photorealistic effects, and compose professional desktop publishing documents. This hands-on resource brings you from concept to completion with examples that span a range of art styles--using the vector drawing program that thinks it's a bitmap editor. With these tutorials that apply to Xara Xtreme, Xtreme Pro, and Magix Xtreme Photo & Graphic Designer, you'll: Work with vector paths that look like paint strokes Tag colors to dramatically change complex drawings in seconds Build multi-page, graphically rich websites in a few hours Convert bitmap web graphics to resizable vector shapes Design artwork in minutes that looks like it took days Create and export original Flash animations for the web in no time Create 3D text and apply special effects to imported photos and vector shapes Invisibly retouch photographs with feathering, fractal fills, multi-step gradients, and transparencies Inside you'll find an inspirational Xara GrandMasters Gallery of award-winning artwork from around the world. Get started today by downloading free trial software from www.xara.com! Download lesson files from www.mhprofessional.com/computingdownload and www.theboutons.com. Gary David Bouton, an international award-winning illustrator, has authored 25 books on graphics software, including CorelDRAW X4: The Official Guide. He practices what he teaches: his work can be seen on Graphics.com, TalkGraphics, The CG Society, and YouTube.

This is an introductory course on the methods of computing asymptotics of probabilities of rare events: the theory of large deviations. The book combines large deviation theory with basic statistical mechanics, namely Gibbs measures with their variational characterization and the phase transition of the Ising model, in a text intended for a one semester or quarter course. The book begins with a straightforward approach to the key ideas and results of large deviation theory in the context of independent identically distributed random variables. This includes Cramér's theorem, relative entropy, Sanov's theorem, process level large deviations, convex duality, and change of measure arguments. Dependence is introduced through the interactions potentials of equilibrium statistical mechanics. The phase transition of the Ising model is proved in two different ways: first in the classical way with the Peierls argument, Dobrushin's uniqueness condition, and correlation inequalities and then a second time through the percolation approach. Beyond the large deviations of independent variables and Gibbs measures, later parts of the book treat large deviations of Markov chains, the Gärtner-Ellis theorem, and a large deviation theorem of Baxter and Jain that is then applied to a nonstationary process and a random walk in a dynamical random environment. The book has been used with students from mathematics, statistics, engineering, and the sciences and has been written for a broad audience with advanced technical training. Appendixes review basic material from analysis and probability theory and also prove some of the technical results used in the text.