Published paper
Abstract
The paper studies actions of epimorphic subgroups on homogeneous spaces, including invariant measures and density properties. Its elementary weak-limit invariance claim is used in the expanding-horosphere proof.
Role in dependence graphs
Proof-critical source
The Dirichlet spectrum
This paper is included only for the following marked statement:
- Claim 3.2 · ETDS 20 (2000), Section 3Invariance of weak limits under the expanding unipotent subgroup.
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Exact reviewed source
Exact version of record hosted by an author · Ergodic Theory and Dynamical Systems 20 (2000), 567–592
Nimish A. Shah and Barak Weiss. On actions of epimorphic subgroups on homogeneous spaces. Ergodic Theory and Dynamical Systems 20 (2000), no. 2, 567–592.
Open audited source ↗01Statements1 reported findingNo statement issues found
Claim 3.2 gives the exact weak-limit invariance principle used by Kleinbock–Weiss.
Claim 3.2No issue found
Contracted conjugates force invariance of every weak limit
Section 3 · exact journal-final copy
If the translated measures converge and conjugating a fixed group element by the translating sequence tends to the identity, then translating the original orbit measure by that element changes every compactly supported test integral by a quantity tending to zero. The weak limit is therefore invariant.
02Proofs1 reported findingNo proof issues found
The selected claim is a self-contained test-function calculation with no further non-book imports.
Proof of Claim 3.2No issue found in the reviewed proof
Uniform continuity on compact support closes the argument
Section 3 · exact journal-final copy
After moving the fixed group element across the translating sequence, the resulting conjugate converges uniformly to the identity on the compact support relevant to the test function. Passing to the weak limit yields invariance. No mixing or measure classification is used in this step.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.