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Probability Spaces with an Infinite Number of Sample Points
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approximation assumed basic Borel bounded called Chapter characteristic function clear collection conditional probability Consider continuous convenient convergence corresponding course covariance defined density derived difference differential discrete discussion distribution function eigenvalue elementary elements equal equation ergodic estimate example exists expectation experiment fact field finite fixed follows Further given hence implies independent indicates inequality infinite integrable interest interval introduced invariant irreducible joint jump linear Markov chain Markovian matrix mean square measure models natural non-negative normal noted Notice obtained occur operator outcomes parameter points positive possible probability distribution probability space problems proof random variables referred relation representation respect result satisfy sequence sigma-field simple space spectral stationary process sufficiently Suppose theorem theory tion transformation transition probability uniformly variance vector zero