Skip to main content
MathOverflow

Return to Answer

Added the assumption that $X$ is standard.
Source Link
burtonpeterj
burtonpeterj
  • 1.8k
  • 9
  • 16

The space of observables is typically not compact when $|F| > 1$. For example, if $|F| = 2$ and $X$ is a nonatomic probability space then the space of observables can be identified with the measure algebra of $X$.

Futhermore, any two nonatomic standard probability spaces are isomorphic and hence under this assumption on $X$ the space of observables depends only on the cardinality of $F$.

The space of observables is typically not compact when $|F| > 1$. For example, if $|F| = 2$ and $X$ is a nonatomic probability space then the space of observables can be identified with the measure algebra of $X$.

Futhermore, any two nonatomic probability spaces are isomorphic and hence under this assumption on $X$ the space of observables depends only on the cardinality of $F$.

The space of observables is typically not compact when $|F| > 1$. For example, if $|F| = 2$ and $X$ is a nonatomic probability space then the space of observables can be identified with the measure algebra of $X$.

Futhermore, any two nonatomic standard probability spaces are isomorphic and hence under this assumption on $X$ the space of observables depends only on the cardinality of $F$.

Source Link
burtonpeterj
burtonpeterj
  • 1.8k
  • 9
  • 16

The space of observables is typically not compact when $|F| > 1$. For example, if $|F| = 2$ and $X$ is a nonatomic probability space then the space of observables can be identified with the measure algebra of $X$.

Futhermore, any two nonatomic probability spaces are isomorphic and hence under this assumption on $X$ the space of observables depends only on the cardinality of $F$.