Titlebook: Measure Theory; J. L. Doob Textbook 1994 Springer Science+Business Media New York 1994 Conditional probability.Distribution.Hilbert space.

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動機

Measurable Functions, closed under limit operations. Similarly, in studying measures, a natural class of admissible sets is a σ algebra, because closure under the operations of complementation and the forming of countable unions and intersections are needed.

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決定性

Conditional Expectation; Martingale Theory,rent concept, probabilists cannot define stochastic processes, but they recognize one when they see it! Typical examples of the application of the term are to martingales and to Markov processes, both defined in this chapter.

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occurrence

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Signed Measures,ction 2 that a signed measure is actually bounded on the side where it is finite. For a signed measure space (., S,λ,), the signed measure λ has its values in (-∞,+∞] if and only if λ(.) > -∞, its values in [-∞,+∞) if and only if λ(.) < +∞, and λ is finite valued if and only if λ(.) is finite.