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If the topology of locally compact topological group G is not discrete, then haar measure of singlton is zero $\mu(\{x\})=0$

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#measure-theory #harmonic-analysis #topological-groups #locally-compact-groups #haar-measure
307
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Haar measures are decomposable

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#measure-theory #harmonic-analysis #topological-groups #locally-compact-groups #haar-measure
230
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Are Haar measures localizable?

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#measure-theory #harmonic-analysis #topological-groups #locally-compact-groups #haar-measure
70
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Is integration with respect to a Radon measure a normal weight on $L^\infty(X)$?

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#measure-theory #c-star-algebras #von-neumann-algebras #locally-compact-groups
75
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Is the Pontryagin map uniformly continuous?

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#harmonic-analysis #topological-groups #uniform-continuity #duality-theorems #locally-compact-groups
71
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Construct an invariant mean from an invariant functional

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#functional-analysis #measure-theory #operator-theory #locally-compact-groups #topological-semigroups
106
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Product of locally Borel subsets is locally Borel

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#general-topology #measure-theory #harmonic-analysis #borel-sets #locally-compact-groups
52
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Is norm-continuous representation factored through a Lie quotient group?

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#representation-theory #operator-algebras #harmonic-analysis #locally-compact-groups
19
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Something similar to the Minkowski's lattice theorem for the locally compact groups (problem with an exercise)

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#quotient-spaces #locally-compact-groups #haar-measure
240
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Real Elliptic curves as compact abelian groups

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#abelian-groups #elliptic-curves #harmonic-analysis #locally-compact-groups #abelian-varieties
21
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Is Fourier transform on compact group dependent on representatives of unitary equivalence class?

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#representation-theory #fourier-transform #harmonic-analysis #locally-compact-groups
306
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Weird duality between integers and p-adic integers

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#abelian-groups #p-adic-number-theory #group-isomorphism #duality-theorems #locally-compact-groups
65
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Subgroups of self dual groups

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#abelian-groups #group-isomorphism #duality-theorems #quotient-group #locally-compact-groups
123
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When is the intersection of all open normal subgroups equal to the connected component at the identity?

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#abelian-groups #connectedness #topological-groups #locally-compact-groups
61
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Non-discrete LCAG's whose closed non-trivial subgroups are open

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#abelian-groups #p-adic-number-theory #group-isomorphism #locally-compact-groups #profinite-groups

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