π-system and monotone class

[hadiSanji]

Assume P is a π-system (that is, P is closed under finite intersections) and M is monotone class (that is M is a non-empty collection of subsets of Ω closed under monotone limits).

Show that P⊂M does not imply σ(P)⊂M.

[BGM]

The complement is not necessary in the monotone class?

[hadiSanji]

HI
please more explain about question. thanks

[BGM]

But I see a lots of reply in other forum

http://math.stackexchange.com/questi...monotone-class

I do not know much about the question, but my first thought is just construct a simple counter example.

I mean that the sigma algebra is also closed under set complement, but not necessary closed in the monotone class and the pi system.