1. Are uncountable unions of sigma algebras on a set X still a sigma algebra on X?(adsbygoogle = window.adsbygoogle || []).push({});

2. Are uncountable intersections of sigma algebras on a set X still a sigma algebra on X? (I think this statement is required to show the existence of sigma algebra generated by a set)

3. If 2 is true, can we use De Morgan's law to show than 1 is true?

4. If 1 is true, why do we require "countable unions" is the definition of sigma algebra?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Definition of sigma algebra

Tags:

Loading...

Similar Threads for Definition sigma algebra |
---|

I Definition of a neighborhood |

I Understanding metric space definition through concrete examples |

I Definition of second-countable |

I Dense set equivalent definitions |

I Directional & Partial Derivatives ... working from the definition |

**Physics Forums | Science Articles, Homework Help, Discussion**