By Daniel Li, Hervé Queffélec
Ce livre est consacré à l'étude des espaces de Banach, en mettant l'accent
sur les liens avec l'Analyse classique, l'Analyse Harmonique, et les
Probabilités. Seules des connaissances usuelles d'Analyse Fonctionnelle de niveau
Maîtrise sont requises, l'étude étant prise à son début. Elle est progressivement
développée de façon approfondie, présentant plusieurs résultats
fondamentaux obtenus dans l. a. période 1950-2000 : Théorème de Grothendieck,
Théorème de Dvoretzky, Théorème de dichotomie de Rosenthal, Théorème de
dichotomie de Gowers, etc., avec certaines de leurs functions.
Daniel Li est Professeur à l'Université d'Artois (Lens). Ses travaux portent
sur l. a. Géométriedesespacesde Banach et l'Analyse Harmonique.
Hervé Queffélec est Professeur à l'Université de Lille 1. Ses travaux portent
sur l'Analyse Harmonique et les méthodes probabilistes en examine.
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2 Duties of care Several judgements have established that employers owe a duty of care to each of their employees. This duty cannot be assigned to others, even if a consultant is employed to advise on health and safety matters or if the employees are sub-contracted to work with another employer. These duties may be sub-divided into four groups. Employers must: S S S S provide provide provide provide a safe place of work safe plant and equipment a safe system of work safe and competent fellow employees.
As mentioned earlier, employers are responsible for the actions of their employees (vicarious liability) provided that the action in question took place during the normal course of their employment. 9 Levels of statutory duty There are three levels of statutory duty which form a hierarchy of duties. These levels are used extensively in health and safety statutory (criminal) law but have been defined by judges under common law. The three levels of duty are absolute, practicable and reasonably practicable.
The prosecution in a criminal case has to prove the guilt of the accused beyond reasonable doubt. While this obligation is not totally removed in health and safety cases, section 40 of the Health and Safety at Work Act 1974 transferred, where there is a duty to do something ‘so far as is reasonably practicable’ or ‘so far as is practicable’ or ‘use the best practicable means’, the onus of proof to the accused to show that there was no better way to discharge his duty under the Act. However, when this burden of proof is placed on the accused, they need only satisfy the court on the balance of probabilities that what they are trying to prove has been done.