Post History
#6: Post edited
by
Ooker
·
2026-05-04T08:28:32Z (5 months ago)
- Assuming I have a dice whose sides are _named_, not _numbered_. Can I have some way to describe the expectation of it? Or must I numbered the events in order to get the mean?
- To put it in another way: why must the [codomain](https://en.wikipedia.org/wiki/Codomain) of the [measure](https://en.wikipedia.org/wiki/Measure_(mathematics)) be $\mathbb R$ (or $\mathbb R \cup \{∞\}$ to be precise), beside practical applications? What properties do we lose or gain if it is not $\mathbb R$? What if the measure is not a [Lebesgue measure](https://en.wikipedia.org/wiki/Lebesgue_measure) as well?
Note that the probability to get each side is still $\frac{1}{6}\in \mathbb R$.
- Assuming I have a dice whose sides are _named_, not _numbered_. Can I have some way to describe the expectation of it? Or must I numbered the events in order to get the mean?
- To put it in another way: why must the [codomain](https://en.wikipedia.org/wiki/Codomain) of the [measure](https://en.wikipedia.org/wiki/Measure_(mathematics)) be $\mathbb R$ (or $\mathbb R \cup \{∞\}$ to be precise), beside practical applications? What properties do we lose or gain if it is not $\mathbb R$? What if the measure is not a [Lebesgue measure](https://en.wikipedia.org/wiki/Lebesgue_measure) as well?
- Note that the probability to get each side is still $\frac{1}{6}\in \mathbb R$.
- Related question: [How important results in classical statistics be generalized when codomain of the measure is not $\mathbb R$?](https://math.codidact.com/posts/296071)
#5: Post edited
by
Ooker
·
2026-05-03T15:39:51Z (5 months ago)
- Assuming I have a dice whose sides are _named_, not _numbered_. Can I have some way to describe the expectation of it? Or must I numbered the events in order to get the mean?
To put it in another way: why must the [codomain](https://en.wikipedia.org/wiki/Codomain) of the [measure](https://en.wikipedia.org/wiki/Measure_(mathematics)) be $\mathbb R$ (or $\mathbb R \cup {∞}$ to be precise), beside practical applications? What properties do we lose or gain if it is not $\mathbb R$? What if the measure is not a [Lebesgue measure](https://en.wikipedia.org/wiki/Lebesgue_measure) as well?- Note that the probability to get each side is still $\frac{1}{6}\in \mathbb R$.
- Assuming I have a dice whose sides are _named_, not _numbered_. Can I have some way to describe the expectation of it? Or must I numbered the events in order to get the mean?
- To put it in another way: why must the [codomain](https://en.wikipedia.org/wiki/Codomain) of the [measure](https://en.wikipedia.org/wiki/Measure_(mathematics)) be $\mathbb R$ (or $\mathbb R \cup \{∞\}$ to be precise), beside practical applications? What properties do we lose or gain if it is not $\mathbb R$? What if the measure is not a [Lebesgue measure](https://en.wikipedia.org/wiki/Lebesgue_measure) as well?
- Note that the probability to get each side is still $\frac{1}{6}\in \mathbb R$.
#4: Post edited
by
Ooker
·
2026-05-03T15:37:59Z (5 months ago)
- Assuming I have a dice whose sides are _named_, not _numbered_. Can I have some way to describe the expectation of it? Or must I numbered the events in order to get the mean?
To put it in another way: why must the [codomain](https://en.wikipedia.org/wiki/Codomain) of the measure be $\mathbb R$, beside practical applications? What properties do we lose or gain if it is not $\mathbb R$? What if the measure is not a [Lebesgue measure](https://en.wikipedia.org/wiki/Lebesgue_measure) as well?- Note that the probability to get each side is still $\frac{1}{6}\in \mathbb R$.
- Assuming I have a dice whose sides are _named_, not _numbered_. Can I have some way to describe the expectation of it? Or must I numbered the events in order to get the mean?
- To put it in another way: why must the [codomain](https://en.wikipedia.org/wiki/Codomain) of the [measure](https://en.wikipedia.org/wiki/Measure_(mathematics)) be $\mathbb R$ (or $\mathbb R \cup {∞}$ to be precise), beside practical applications? What properties do we lose or gain if it is not $\mathbb R$? What if the measure is not a [Lebesgue measure](https://en.wikipedia.org/wiki/Lebesgue_measure) as well?
- Note that the probability to get each side is still $\frac{1}{6}\in \mathbb R$.
#3: Post edited
by
Ooker
·
2026-05-03T15:35:06Z (5 months ago)
- Assuming I have a dice whose sides are _named_, not _numbered_. Can I have some way to describe the expectation of it? Or must I numbered the events in order to get the mean?
To put it in another way: why must the [codomain](https://en.wikipedia.org/wiki/Codomain) of the measure be , beside practical applications? What characteristics do we lose or gain if it is not $\mathbb R$? What if the measure is not a [Lebesgue measure](https://en.wikipedia.org/wiki/Lebesgue_measure) as well?- Note that the probability to get each side is still $\frac{1}{6}\in \mathbb R$.
- Assuming I have a dice whose sides are _named_, not _numbered_. Can I have some way to describe the expectation of it? Or must I numbered the events in order to get the mean?
- To put it in another way: why must the [codomain](https://en.wikipedia.org/wiki/Codomain) of the measure be $\mathbb R$, beside practical applications? What properties do we lose or gain if it is not $\mathbb R$? What if the measure is not a [Lebesgue measure](https://en.wikipedia.org/wiki/Lebesgue_measure) as well?
- Note that the probability to get each side is still $\frac{1}{6}\in \mathbb R$.
#2: Post edited
by
Ooker
·
2026-05-03T15:31:00Z (5 months ago)
Assuming I have a dice whose sides are _named_, not _numbered_. Can I have some way to describe the expectation of it? Or must I numbered the events in order to get the mean?To put it in another way: why must the [codomain](https://en.wikipedia.org/wiki/Codomain) of the measure be $\mathbb R$, beside practical applications? What characteristics do we lose or gain if it is not $\mathbb R$? What if the measure is not a [Lebesgue measure](https://en.wikipedia.org/wiki/Lebesgue_measure) as well?
- Assuming I have a dice whose sides are _named_, not _numbered_. Can I have some way to describe the expectation of it? Or must I numbered the events in order to get the mean?
- To put it in another way: why must the [codomain](https://en.wikipedia.org/wiki/Codomain) of the measure be , beside practical applications? What characteristics do we lose or gain if it is not $\mathbb R$? What if the measure is not a [Lebesgue measure](https://en.wikipedia.org/wiki/Lebesgue_measure) as well?
- Note that the probability to get each side is still $\frac{1}{6}\in \mathbb R$.
#1: Initial revision
by
Ooker
·
2026-05-03T08:37:53Z (5 months ago)
Can expectation be calculated if the events aren't numbered?
Assuming I have a dice whose sides are _named_, not _numbered_. Can I have some way to describe the expectation of it? Or must I numbered the events in order to get the mean? To put it in another way: why must the [codomain](https://en.wikipedia.org/wiki/Codomain) of the measure be $\mathbb R$, beside practical applications? What characteristics do we lose or gain if it is not $\mathbb R$? What if the measure is not a [Lebesgue measure](https://en.wikipedia.org/wiki/Lebesgue_measure) as well?