Let (X) be an arbitrary set and (mathscr{F} subset mathscr{P}(X)). Show that [sigma(mathscr{F})=bigcup{sigma(mathscr{C}): mathscr{C} subset mathscr{F} text

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Let $X$ be an arbitrary set and $\mathscr{F} \subset \mathscr{P}(X)$. Show that

\[\sigma(\mathscr{F})=\bigcup\{\sigma(\mathscr{C}): \mathscr{C} \subset \mathscr{F} \text { countable sub-family }\}\]

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Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

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Question Posted: Jan 23, 2024 10:00 AM

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Let (X) be an arbitrary set and (mathscr{F} subset mathscr{P}(X)). Show that [sigma(mathscr{F})=bigcup{sigma(mathscr{C}): mathscr{C} subset mathscr{F} text

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Write o 6 C CF C is a countable subfamily If C C F we get o 6 CoF and so C G F Conversely it ...View the full answer

Measures Integrals And Martingales

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