I am reading one book and the author presents what he calls a distributivity formula:...

Gretchen Schwartz

Gretchen Schwartz

Answered

2022-07-01

I am reading one book and the author presents what he calls a distributivity formula:
j J i I j F i j = { i j } K j J F i j j
where K = Π j J I j (the set of all sequences { i j , j J}).
My question is regarding the notation. The LHS is quite clear to me. However, I'm now sure what are actually the members of K. Say J = { 1 , 2 , } and I j = { 1 , 2 , }. What is actually i j here?

Answer & Explanation

Marisol Morton

Marisol Morton

Expert

2022-07-02Added 13 answers

On the RHS, we are finding the intersection of j J F i j j . Here, the i j is the values for which we are intersecting; it says { i j } K. If J = { 1 , 2 , 3 , }, then K = I 1 × I 2 × I 3 ×

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