Jeans theorem

Target entity: Jeans theorem
Context triple: [virial theorem, relatedTo, Jeans theorem]

• A. Cauchy's theorem in group theory
  Cauchy's theorem in group theory is a fundamental result stating that if a finite group’s order is divisible by a prime p, then the group contains an element (and hence a subgroup) of order p.
• B. Peter–Weyl theorem
  The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
• C. Schur’s lemma
  Schur’s lemma is a fundamental result in representation theory stating that any homomorphism between irreducible representations is either zero or an isomorphism, and that endomorphisms of an irreducible representation over an algebraically closed field are scalar multiples of the identity.
• D. Janet–Cartan theorem
  The Janet–Cartan theorem is a fundamental result in differential geometry stating that any real-analytic Riemannian manifold can be locally isometrically embedded into a Euclidean space of sufficiently high dimension.
• E. Noether's isomorphism theorems
  Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Jeans theorem
Target entity description: Jeans theorem is a fundamental result in stellar dynamics stating that any steady-state solution of the collisionless Boltzmann equation depends on phase-space coordinates only through integrals of motion.

• A. Cauchy's theorem in group theory
  Cauchy's theorem in group theory is a fundamental result stating that if a finite group’s order is divisible by a prime p, then the group contains an element (and hence a subgroup) of order p.
• B. Peter–Weyl theorem
  The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
• C. Schur’s lemma
  Schur’s lemma is a fundamental result in representation theory stating that any homomorphism between irreducible representations is either zero or an isomorphism, and that endomorphisms of an irreducible representation over an algebraically closed field are scalar multiples of the identity.
• D. Janet–Cartan theorem
  The Janet–Cartan theorem is a fundamental result in differential geometry stating that any real-analytic Riemannian manifold can be locally isometrically embedded into a Euclidean space of sufficiently high dimension.
• E. Noether's isomorphism theorems
  Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
• F. None of above. chosen