Question

Showing a distance function is a metric.

score 998 · Answer 1 · 2026-05-14 23:22:49

998

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Showing a distance function is a metric.

Published on 14 May 2026 - 23:22

score 71 · Answer 2 · 2026-04-16 18:57:17

71

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$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$

Published on 16 Apr 2026 - 18:57

score 1.5k · Answer 3 · 2026-04-14 01:54:24

1.5k

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$\delta : C([0,1])\to\mathbb{R}$, $f\mapsto f(0)$, with sup-norm is bounded but unbounded with one-norm.

Published on 14 Apr 2026 - 1:54

score 46 · Answer 4 · 2026-05-15 11:17:13

46

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What examples are there of sets with locally non-extreme measure?

Published on 15 May 2026 - 11:17

score 36 · Answer 5 · 2026-05-15 23:53:32

36

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Find all real numbers satisfying 3 conditions with sums

Published on 15 May 2026 - 23:53

score 1.8k · Answer 6 · 2026-05-14 20:54:05

1.8k

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convex hull of union convex set

Published on 14 May 2026 - 20:54

score 38 · Answer 7 · 2026-05-15 11:17:14

38

Views

How do I evaluate the the nth root of Lebesgue measure of a ball

Published on 15 May 2026 - 11:17

score 127 · Answer 8 · 2026-04-15 09:42:05

True or false: A function $f$ defined on an interval $I$ is continuous if the image of each interval $I_0 \subset I$ is an interval

score 133 · Answer 9 · 2026-04-14 05:41:23

133

Views

Is the restriction of a projection to a measurable subset measure preserving?

Published on 14 Apr 2026 - 5:41

score 143 · Answer 10 · 2026-05-15 23:53:52

143

Views

A nowhere dense set containing arbitrarily close arithmetic progressions

Published on 15 May 2026 - 23:53

score 44 · Answer 11 · 2026-05-11 08:41:57

44

Views

$\int_0^1 \log f(t)dt \le \int_0^1 \log g(t)dt$ implies $\int_0^1 \log (f(t)+1)dt \le \int_0^1 \log (g(t)+1)dt$?

Published on 11 May 2026 - 8:41

score 89 · Answer 12 · 2026-04-15 08:41:59

89

Views

Is this sequence of functions uniformly convergent on [0, 2] ??

Published on 15 Apr 2026 - 8:41

score 133 · Answer 13 · 2026-05-15 11:16:42

133

Views

An integrable function f and a bounded function g that disagree at a set with measure 0, but g is not integrable.

Published on 15 May 2026 - 11:16

score 46 · Answer 14 · 2026-04-24 11:27:39

For $a\in R$ . calculate $\lim\limits_{n\to\infty}\frac{1}{n}$( $( a+\frac{1}{n})^2 + (a +\frac{2}{n})^2+.....+( a + \frac{n-1}{n})^2$)

score 131 · Answer 15 · 2026-05-13 17:08:18

131

Views

Taking the limit of n(e^1/n −1) as n approaches infinity then proving it by the squeeze theorem

Published on 13 May 2026 - 17:08

List Question

Showing a distance function is a metric.

$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$

$\delta : C([0,1])\to\mathbb{R}$, $f\mapsto f(0)$, with sup-norm is bounded but unbounded with one-norm.

What examples are there of sets with locally non-extreme measure?

Find all real numbers satisfying 3 conditions with sums

convex hull of union convex set

How do I evaluate the the nth root of Lebesgue measure of a ball

True or false: A function $f$ defined on an interval $I$ is continuous if the image of each interval $I_0 \subset I$ is an interval

Is the restriction of a projection to a measurable subset measure preserving?

A nowhere dense set containing arbitrarily close arithmetic progressions

$\int_0^1 \log f(t)dt \le \int_0^1 \log g(t)dt$ implies $\int_0^1 \log (f(t)+1)dt \le \int_0^1 \log (g(t)+1)dt$?

Is this sequence of functions uniformly convergent on [0, 2] ??

An integrable function f and a bounded function g that disagree at a set with measure 0, but g is not integrable.

For $a\in R$ . calculate $\lim\limits_{n\to\infty}\frac{1}{n}$( $( a+\frac{1}{n})^2 + (a +\frac{2}{n})^2+.....+( a + \frac{n-1}{n})^2$)

Taking the limit of n(e^1/n −1) as n approaches infinity then proving it by the squeeze theorem

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