# Elementary point about measurable cards

1. Jul 29, 2014

Just refreshing my understanding of measurable cardinals, the first step (more questions may follow, but one step at a time) is to make sure I understand the conditions: one of them is

For a (an uncountable) measurable cardinal κ, there exists a non-trivial, 0-1-valued measure μ on P(κ) such that there exists an λ<κ such that for any sequence [Aα: α<λ ] of disjoint sets Aα whose elements are smaller-than-κ ordinals, μ($\cup${ Aα }) = ∑μ(Aα)

Would not this mean that there would be a β<λ such that μ(Aβ) = 1 and $\forall$γ<λ, (γ≠ β $\Rightarrow$ μ(Aβ) = 0)?

If not, why not?

P.S. except of course for those sequences for which for all α in the set of indices of the sequence, μ(Aα)=0

Last edited: Jul 29, 2014
2. Aug 3, 2014