Criteria for compactness and for discreteness of locally compact amenable groups
Criteria for compactness and for discreteness of locally compact amenable groups
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a locally compact group <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P left-parenthesis upper G right-parenthesis equals left-brace 0 less-than-over-equals phi element-of upper L 1 left-parenthesis upper G right-parenthesis semicolon integral phi left-parenthesis x right-parenthesis d x …