- #1

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What is the difference between the integrable set-valued maps and integrable single-valued map?

With illustrative examples, if possible?

Thank you very.

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- Thread starter moh salem
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- #1

- 21

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What is the difference between the integrable set-valued maps and integrable single-valued map?

With illustrative examples, if possible?

Thank you very.

- #2

mathman

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- #3

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[tex]Let \text{ }F:X\longrightarrow P(Y) \text{ }be \text{ }a \text{ }set-valued \text{ }map \text{ }and \text{ } f:X\longrightarrow Y \text{ }be \text{ }a \text{ }measurable\\ \text{ }single-valued \text{ }map, \text{ }where \text{ } F(x)=\{f(x)\}.\\ Is \text{ }F \text{ }be \text{ }a \text{ }measurable. \text{ }And \text{ }do \text{ }the \text{ }conversely \text{ }is \text{ }true .[/tex]

- #4

mathman

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- #5

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Let

for examples,

(1) Let

(2) Let

(3) Let

- #6

mathman

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In my experience, measure is a set function, but integrability refers to point functions.

- #7

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Thanks mathman.

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