## Algebraic Combinations of Continuous Flows |

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2(<p)-measurable subset binary operation Borel measure Borel set Borel subset choose clear common upper bound compatible members completes the proof continuous function countable intersection countable set denote Distributive Law f rep family Rep+(<p flow follows at once follows from Theorem ft(uiJj harmonic sum Hausdorff space Hausdorff space X ijj and tt ijj TT ijj v tt ijj2 ijj3 implies infimum inv f isotonic left ramming point Lemma let f let ijj let ip Let jl maximum measurable function measurable subset members of Rep*(<p metric space mutually singular nonnegative function defined nonnegative measures defined nonnegative quasi multipliers once from Theorem open subset p-orbit partition positive integer proof of Theorem pseudo-maximum Q(tt quasi-flow satisfies si-flow strictly increasing tt are compatible tt e Rep+(<p tt exists tt-multiplier u v v u<p and v<p uijj v<p are compatible x e Q(iJj