Chapter 1: Problem 20
Suppose \(\mathcal{D}\) is a nonempty collection of subsets of \(\mathcal{C}\). Consider the collection of events, $$\mathcal{B}=\cap\\{\mathcal{E}: \mathcal{D} \subset \mathcal{E} \text { and } \mathcal{E} \text { is a } \sigma \text { -field }\\}$$ Note that \(\phi \in \mathcal{B}\) because it is in each \(\sigma\) -field, and, hence, in particular, it is in each \(\sigma\) -field \(\mathcal{E} \supset \mathcal{D}\). Continue in this way to show that \(\mathcal{B}\) is a \(\sigma\) -field.
Short Answer
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.