/sci/ - Science & Math

>>11847277
>>11847330

>>11736762
something something american math students only plug in numbers at random something

>>11730243
Please try to write a coherent phrase next time, thank you.

I don't know, but now I have an urge to mate with about half of them.

>>10123106
how do I prove this by the way

Trying to prove that if [math]f\geq 0[/math] is Lebesgue integrable on [math] [a,b] [/math] (unbounded), then [math]cf[/math] is also Lebesgue integrable.
The definition for Lebesgue integrability I'm using in this case for [math]f\geq 0[/math] is that [math]{^{N}f(x)} = \begin{cases} f(x),& 0\leq f(x) \leq N \\ N,& f(x) > N \end{cases} [/math] is measurable for all [math]N[/math] and [math]\lim_{N\to \infty} \int_{a}^{b} {^{N}f(x)} [/math] converges.
My attempt: for [math]c>0[/math], let [math]N^{\prime}=cN[/math]. Then [math]{^{N^{\prime}}cf(x)} = \begin{cases} cf(x),& 0\leq cf(x) \leq N^{\prime} \\ N^{\prime},& cf(x) > N^{\prime} \end{cases} [/math] is also measurable, since measurability of a function is closed under multiplication. Further, since [math]\lim_{N\to \infty} \int_{a}^{b} {^{N}f(x)} [/math] converges, [math]\lim_{N\to \infty} \int_{a}^{b} {^{N}cf(x)} = c\cdot \lim_{N\to \infty} \int_{a}^{b} {^{N}f(x)}[/math] , which is the desired result.
I think the argument is similar for [math]c<0[/math] and [math]c=0[/math], but I'm not sure if I'm overlooking anything.

bümping to limit +1

>>10006161

>>9995093
>needing to write to learn math

>>9798221
>math is just computations

>>9699232
It shouldn't surprise anyone that these OPs are always retards

>"Z"
>""F""
>"""C"""

>>9576551
Biology
>I like da animals

>>9569782
speed light is constant and never changes?

This thread is for questions that don't deserve their own thread.

Tips!
>give context
>describe your thought process if you're stuck
>try wolframalpha.com and stackexchange.com
>How To Ask Questions The Smart Way http://www.catb.org/~esr/faqs/smart-questions.html

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