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Structure of generated sigma algbra

  1. Mar 12, 2015 #1
    I am think what is the structure of generated ##\sigma##-algebra. Let me make it specific. How to represent ##\sigma(\mathscr{A})##, where ##\mathscr{A}## is an algebra. Can I use the elements of ##\mathscr{A}## to represent the element in ##\sigma(\mathscr{A})##?
     
  2. jcsd
  3. Mar 13, 2015 #2

    Stephen Tashi

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    That is an interesting question. We could make it even more specific. Is each [itex] S \in \sigma(\mathscr{A}) [/itex] representable as [itex] S = lim_{n \rightarrow \infty} ( \cup_{i=0}^n A_i ) [/itex] where [itex] A_i \in \mathscr{A} [/itex] ? (I don't claim to know the answer, but it seems like a good place to start.)
     
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