#Measure Theory

12 messages · Page 1 of 1 (latest)

autumn emberBOT
flat sirenBOT
#

tautau
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tautau
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tidal dagger
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We define the set
[
X = { x \in \mathbb{R}^2 : |x_1| + |x_2| < 1 }
]
and the measure
[
\mu(A) = m_2(A \cap X) \quad \text{for } A \in \mathcal{B}(\mathbb{R}^2),
]
where ( m_2 ) denotes the Lebesgue measure on ( \mathbb{R}^2 ).

Can (\mu) be represented as a product measure, (\mu = \mu_1 \times \mu_2), where (\mu_1) and (\mu_2) are Borel measures on (\mathbb{R})?

flat sirenBOT
#

tautau

419212360985608193.png
tidal dagger
#

may somebody help me with my HW thanks 🙂

hexed goblet
#

Deleting your original question and putting 5 replies makes it look like your question has been answered and you've abandoned the thread, just fyi.

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For this question, have you tried anything?

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I think the majority of this question is just understanding the words.

#

You also need to know what X looks like.

tidal dagger
#

ohh i didnt know that i postet the wrong stuff :/ and yes i have tried something but somehow i dont get to a conclusion i dont even know yet if such a produkt exists

hexed goblet