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Titlebook: Measure, Integral and Probability; Marek Capiński,Peter Ekkehard Kopp Textbook 19991st edition Springer-Verlag London 1999 Analysis.Integr

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Textbook 19991st editionis not wholly secure; yet they provide the principal model for the development of the abstract measure spaces which underpin modern probability theory, while the Lebesgue function spaces remain the main sour ce of examples on which to test the methods of functional analysis and its many applications
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Spaces of integrable functions,ntegrable function as a ‘point’ in a function space, or, more precisely, as an element of a .. For this we need some extra structure on the space of functions we deal with, and we need to come to terms with the fact that the measure and integral cannot distinguish between functions which are almost everywhere equal.
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Motivation and preliminaries,where we have to sift a great deal of prior information, and those where we have little to go on. Some degree of judgement is needed in all cases; but we seek an orderly theoretical framework and methodology which enables us to formulate general laws in quantitative terms.
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