A characterization of quasi <mml:math alttext="$r^* $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>-invariant measures on metric topological semigroups is obtained by showing that their support has a left group structure thus generalizing previously known results for relatively <mml:math alttext="$r^* $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>-invariant measures and the topo-algebraic structure of their support.

A note on quasi <mml:math alttext="$R^* $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>-invariant measures on semigroups

A note on quasi <svg style="vertical-align:-0.1092pt" height="13.8875" version="1.1" viewBox="0 0 18.674999 13.8875" width="18.674999" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,13.688)"><path id="x1D445" d="M627 18l-10 -26q-79 6 -116 27t-69 76q-41 71 -71 138q-13 29 -27.5 39t-42.5 10h-46l-27 -145q-13 -74 -2.5 -88.5t78.5 -20.5l-6 -28h-271l5 28q66 6 82.5 21.5t30.5 87.5l71 387q12 66 2 78.5t-77 19.5l8 28h233q102 0 147 -29q65 -43 65 -129q0 -69 -45.5 -117&#xA;t-115.5 -72q40 -86 66 -133q39 -68 65 -101q28 -37 73 -51zM491 483q0 67 -33.5 101t-91.5 34q-35 0 -51 -10q-13 -8 -20 -48l-45 -245h49q71 0 113 28q79 52 79 140z" /></g><g transform="matrix(.012,-0,0,-.012,11.013,5.525)"><path id="x2217" d="M471 153q-22 -15 -61 -13q-25 31 -45.5 49.5t-56.5 41.5q4 -71 28 -134q-17 -33 -42 -46q-24 12 -42 46q24 63 28 134q-36 -23 -56.5 -41.5t-45.5 -49.5q-36 -2 -61 13q0 28 19 59q65 10 130 43q-65 33 -130 43q-19 31 -19 59q22 15 61 13q25 -31 45.5 -49.5t56.5 -41.5&#xA;q-4 71 -28 134q17 33 42 46q24 -12 42 -46q-24 -63 -28 -134q36 23 56.5 41.5t45.5 49.5q36 2 61 -13q0 -28 -19 -59q-65 -10 -130 -43q65 -33 130 -43q19 -31 19 -59z" /></g></svg>-invariant measures on semigroups

International Journal of Mathematics and Mathematical Sciences

A note on quasi R*-invariant measures on semigroups

Abstract

Copyright