Hello,

For one of the integration questions I have to do, I need to show that

is Lebesgue integrable, where1is the indicator function, and that

.

Does anyone have any ideas about how I would solve this? Thanks for any help!

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- Mar 8th 2010, 03:11 PMcharlotte12Lebesgue integration question
Hello,

For one of the integration questions I have to do, I need to show that

is Lebesgue integrable, where**1**is the indicator function, and that

.

Does anyone have any ideas about how I would solve this? Thanks for any help! - Mar 9th 2010, 03:27 AMOpalg
To see that is Lebesgue-integrable, show that is dominated by some multiple of . (Notice that is bounded as .)

To calculate the integral, let . Differentiate twice under the integral sign to see that . You can evaluate that integral (integration by parts twice) to get . Then integrate twice, using the fact that to get the constants of integration, and you will find that .