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Could someone clarify?

- Thread starter jdinatale
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- #1

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Could someone clarify?

- #2

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- #3

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My apologies,

##E## is a measurable set.

##S_0(E)## is the set of simple functions on ##E##.

The canonical representation of ##\phi \in S_0(E)## is a linear combination of characteristic functions ##\phi = \sum_{i=1}^na_i\mathcal{X}_{E_i}##.

- #4

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I'm guessing there is more to the definition of canonical representation. Maybe you are given that the ##A_i## are disjoint with each other and ##B_j## similarly. And if ##\cup_i A_i = E## and ##\cup_j B_j = E## that would explain those equations.My apologies,

##E## is a measurable set.

##S_0(E)## is the set of simple functions on ##E##.

The canonical representation of ##\phi \in S_0(E)## is a linear combination of characteristic functions ##\phi = \sum_{i=1}^na_i\mathcal{X}_{E_i}##.

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