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STUDY COMPANION
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Probability, measure. Start with outcomes. Decide which sets are events.
Chapter 1 Sections 1.1–1.3 168 source-checked entries
THE PATH THROUGH THESE SECTIONS Allowed sets → Consistent mass → Observations & laws → Integration & limits
1.1 · PROBABILITY SPACES, MEASURES AND σ-ALGEBRAS
1.1.1 The probability space The sample space $\Omega$ contains outcomes $\omega$. Its power set $2^\Omega$ contains all subsets. The event space $\mathcal F\subseteq2^\Omega$ specifies which subsets may receive probabilities. We begin with the structure required of $\mathcal F$.
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CONTINUE IN ORDER
Next: independence and product measures Sections 1.1–1.3 are complete. Continue next at Definition 1.4.1, p. 54.
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Source, editorial choices & storage Amir Dembo, Probability Theory: STAT310/MATH230 , April 23, 2019, printed/PDF pp. 7–54. Statements checked against rendered pages of the supplied 230anotes.pdf. Entry titles, explanations, visuals, and solutions are companion material. The split reader presents the unchanged original PDF alongside companion material. Source notation clarifications appear beside the affected entries. Unnumbered remarks are retained in context; source forward references and substantive source issues are identified explicitly.
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PROBABILITY · A VISUAL NOTEBOOK / SECTIONS 1.1–1.3