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- I need help in order to fully understand the implications of Axler's definition of a ##\sigma##-algebra ... ...

I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ...

I need help in order to fully understand the implications of Axler's definition of a ##\sigma##-algebra ... ...

The relevant text reads as follows:

Now in the above text Axler implies that the set of all subsets of ##\mathbb{R}## is not a ##\sigma##-algebra ... ...

... BUT ... which of the three bullet points of the definition of a ##\sigma##-algebra is violated by the set of all subsets of ##\mathbb{R}## ... and how/why is it violated ...

Help will be much appreciated ...

Peter

I need help in order to fully understand the implications of Axler's definition of a ##\sigma##-algebra ... ...

The relevant text reads as follows:

Now in the above text Axler implies that the set of all subsets of ##\mathbb{R}## is not a ##\sigma##-algebra ... ...

... BUT ... which of the three bullet points of the definition of a ##\sigma##-algebra is violated by the set of all subsets of ##\mathbb{R}## ... and how/why is it violated ...

Help will be much appreciated ...

Peter