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Titlebook: Introduction to Probability and Measure; K. R. Parthasarathy Book 2005 Hindustan Book Agency (India) 2005

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Hilbert Space and conditional Expectation, in our subject. In fact all statistical problems which centre around ‘extrapolation’ or ‘prediction’ are based on the fundamental properties of the space .(.). To elaborate on this theme we shall develop the barest minimum of the theory of Banach and Hilbert spaces.
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Weak Convergence of Probability Measures,ic space . we shall write . for the borel .-algebra of subsets of .. We shall denote by .(.) the space of all bounded real valued continuous functions on . and .(.) the space of all probability measures on ..
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Measures on Product Spaces,pecial cases of such a construction. Later we shall see how integration in the product space is reduced to successive integration over the marginal spaces. When the transition measures happen to be transition probability measures they acquire a practical significance of great value and form the foundations of the study of Markov processes.
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Hilbert Space and conditional Expectation, in our subject. In fact all statistical problems which centre around ‘extrapolation’ or ‘prediction’ are based on the fundamental properties of the space .(.). To elaborate on this theme we shall develop the barest minimum of the theory of Banach and Hilbert spaces.
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Weak Convergence of Probability Measures,ic space . we shall write . for the borel .-algebra of subsets of .. We shall denote by .(.) the space of all bounded real valued continuous functions on . and .(.) the space of all probability measures on ..
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