Elementary point about measurable cards

[nomadreid]

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 [A_α: α<λ ] of disjoint sets A_α whose elements are smaller-than-κ ordinals, μ($\cup${ A_α }) = ∑μ(A_α)

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

 

[Greg Bernhardt]

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

 

[mathman]

"measurable cardinal" is an extremely specialized concept. I am not surprised as the lack of response. I had to look it up on Wikipedia to get an inkling of what means.