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Questions tagged [real-analysis]

For questions about real analysis, a branch of mathematics dealing with limits, convergence of sequences, construction of the real numbers, least upper bound property and related analysis topics, such as continuity, differentiation, and integration through the Fundamental Theorem of Calculus.

8
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0answers
184 views
+100

Potential for Monotone Operator

I have a question about understanding the proof of Theorem 4.11 in the paper A Potential Theory for Monotone Multivalued Operators (accessible here). The authors claim to construct a convex ...
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vote
0answers
100 views
+50

Exercise about convolution of functions

I have found this excercise in theory of convolution (I started it the last week). I have been thinking about it for two days but I don't get solve it: Let be $1<p<2<q<\infty$ and $f:\...
2
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1answer
77 views
+100

must a measure-preserving and order-preserving bijection have measurable inverse?

Let $E$ and $F$ be measurable subsets of $\mathbb{R}$ endowed with the Lebesgue measure $\lambda$. We say that $m:E\to F$ is measure-preserving if for each measurable subset $A$ of $F$, the set $m^{-...
2
votes
1answer
71 views
+50

Show that the density of Random Variable $Y=aX+b$ exists and if $X$ ~$\mathcal{N}(\mu,\sigma^{2})$ then how is $Y$ distributed

Let $X$ be a real random variable and $f$ the density belonging to $X$. Let $a\neq0$, and $b \in \mathbb R$, while $Y:=aX+b$. Show: i) The density of $Y$ wrt the lebesgue measure exists and is $g(x):=...
9
votes
1answer
227 views
+200

Has the Riemann Rearrangement Theorem ever helped in computation rather than just being a warning?

A decent course in elementary analysis will eventually discuss series, absolute convergence, conditional convergence, and the Riemann Rearrangement Theorem. However, in any presentation I've seen, in ...