Gerald Edgar
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Registered User
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1d |
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Counterexample of non-negative sequence weakly converging in $\mathscr{M}^1$ but not $L^1$ added 849 characters in body; added 21 characters in body |
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1d |
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Can an uniformly picked real number be an integer? added 4 characters in body |
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1d |
answered | Can an uniformly picked real number be an integer? |
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1d |
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Counterexample of non-negative sequence weakly converging in $\mathscr{M}^1$ but not $L^1$ added 50 characters in body; edited body |
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1d |
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Counterexample of non-negative sequence weakly converging in $\mathscr{M}^1$ but not $L^1$ added 444 characters in body; added 151 characters in body; edited body; deleted 16 characters in body; added 17 characters in body |
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1d |
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Counterexample of non-negative sequence weakly converging in $\mathscr{M}^1$ but not $L^1$ added 189 characters in body; added 174 characters in body |
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1d |
answered | Counterexample of non-negative sequence weakly converging in $\mathscr{M}^1$ but not $L^1$ |
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2d |
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Is there a known bound in prime gaps? added 1023 characters in body |
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May 22 |
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What is the corresponding version in the complex space of this proposition got in the real space real TeX improved |
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May 21 |
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objects which can’t be defined without making choices but which end up independent of the choice ...easy to construct an algebraic closure... you mean as a subset of the complex numbers? |
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May 20 |
answered | What’s the definition of continuous of set-valued functions? |
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May 15 |
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Approximate closed-form solution for a recurrence Needs some motivation or reason anyone should care about it. Perhaps some interpretation involving a random walk or ??. |
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May 15 |
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Density of a difference set of a set wih zero upper Banach density edited body; edited body; edited body; added 6 characters in body |
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May 15 |
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Principal value of integral added 1086 characters in body; added 2 characters in body; deleted 13 characters in body |
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May 14 |
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Existence of dominating measure for weak*-compact set of measures So the set $\{\delta_x : x \in [0,1]\}$ is not compact; it is discrete. |
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May 14 |
answered | Principal value of integral |
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May 14 |
answered | The pth power of a distance function is twice continuously differentiable, for $p>2$? |
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May 14 |
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Principal value of integral @Carlo: that is perhaps a sensible definition. Can you cite a textbook that uses that definition? |
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May 14 |
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Can an accumulation point be an eigenvalue? $0$ is always in the spectrum (for a compact operator on an infinite-dimensional Hilbert space). For some such operators $0$ is an eigenvalue, but for others it is not. |
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May 14 |
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Principal value of integral Since there are multiple poles, I do not know what "principal value" means. Perhaps you can provide a definition? |
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May 13 |
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Higher dimensional convex hull For your first paragraph, specify that $S$ is a finite set. Then vertex and edge make sense. |
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May 13 |
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Existence of dominating measure for weak*-compact set of measures @Lutz... you are right. Because andy has the wrong definition for the weak* topology. The usual way to define it is to use only continuous $Z$. If we use all measurable $Z$, as andy does, then you get a much stronger topology. Moreover, andy didn't even say that $Z$ should be bounded. So, let's give him a chance to say whether he wants to correct the definition. |
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May 13 |
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Existence of dominating measure for weak*-compact set of measures Indeed, in Davide's example, the map $x \mapsto \delta_x$ is a homeomorphism from $[0,1]$ onto $\mathcal P$. |
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May 12 |
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polynomial zero within a square $p(z)=z^8+k$, for $k$ large, has no zeros inside a large square. But still $|p(0)|$ smaller than the specified points on the unit square. |
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May 12 |
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polynomial zero within a square Try polynomial $z^8+2$. |
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May 12 |
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Prove that the sum of a certain infinite series is 1 Denominator 16 ... maybe it is somehow related to these: en.wikipedia.org/wiki/… |
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May 12 |
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continuty of volume of a convex set in Rn If convexity is not required, then there are simpler counterexamples. The unit cube is the limit of a sequence of finite sets. |
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May 12 |
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continuty of volume of a convex set in Rn If you mean for $L$ to be convex, add that to the text of the question. Then we can use the fact that the boundary of a convex set has measure zero. |
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May 10 |
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Closed form for derivatives $\zeta^{(n)}(1/2)$ Let's hope we get an answer here. Things on Mathworld (and Wikipedia, and so on) stated without citation are not entirely reliable... |
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May 10 |
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Leibnizian calculus textbook @Aerik: It is my experience that in elementary courses (like calculus) it is a Bad Idea to deviate from the textbook in any way. |
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May 10 |
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What Are Some Naturally-Occurring High-Degree Polynomials? "Cubic polynomial occurs" and "Need the cubic formula" are two quite different things. |
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May 8 |
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Functional equations Umar didn't say what is the domain of $f$. Perhaps pairs $(x,x)$ never belong to that domain. |
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May 8 |
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How long can it take to generate a $\sigma$-algebra? Countable unions are not enough. You will also need either complements or countable intersections. |
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May 8 |
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radon-nikodým property of $\ell^\infty$ $l^\infty$ has a subspace isometric to $l^1$. Indeed $l^\infty$ has a subspace isometric to any given separable space. |
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May 6 |
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Borel ideals on $\omega$ are meager? All sets not containing $0$ ... that's an ideal, right? And Borel. In fact clopen. So not meager. |
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May 2 |
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Is every submartingale a convex function of a martingale? Real values? Same filtration? |
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May 2 |
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What fields can be used for an inner product space? added 715 characters in body |
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May 2 |
answered | What fields can be used for an inner product space? |
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May 2 |
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What fields can be used for an inner product space? One could easily define an inner product for a vector space over a formally real field en.wikipedia.org/wiki/Formally_real_field ... Your condition would then be $\langle \mathbf{x},\mathbf{x}\rangle \ne 0$ for nonzero vectors $\mathbf x$. |
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May 2 |
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Identity of binomial series with factorial. edited body |
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Apr 29 |
accepted | Identity of binomial series with factorial. |
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Apr 29 |
answered | Identity of binomial series with factorial. |
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Apr 29 |
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A question on the Mahler conjecture Comment edits are **Coming Soon**(TM) when MO switches to version 2 Stackoverflow software. |
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Apr 27 |
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When does the finite union of convex sets have a hole in it? So it is actually a union and not an intersection? |
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Apr 26 |
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Continuous automorphisms of Q* We have some over-eager question-closers. Unless they tell us why they closed it, we may never know. Maybe they saw that the only tag is "group-theory" and closed it on that basis? |
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Apr 26 |
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Continuous automorphisms of Q* Yes, as Will hints, $\mathbb R^\ast$ is complete in the natural uniform structure for the group. His metric is one that corresponds to this uniform structure. Instead of $|x-y|<\epsilon$ in the definition of "uniformly continuous" you can use $|xy^{-1}-1|<\epsilon$ |
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Apr 26 |
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Is function from topological group to metric space Borel? Pseudo-metrizable but not metrizable means not Hausdorff, right? In a topological group that is not Hausdorff, the closure of a single point is more than the point. And the closure of a subgroup is a subgroup. |
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Apr 25 |
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Formalization (and background) of a formula, concering the integral points of a polygon. I guess the one-dimensional version of this relies on Euler's sum $$\sum_{k=-\infty}^{+\infty} x^k = 0$$ |
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Apr 24 |
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A Model where Dedekind Reals and Cauchy Reals are Different Vote to close until Jean explains what the question means. |
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Apr 24 |
answered | Continuous automorphisms of Q* |
