SOME ALGEBRAIC AND MEASURE THEORETIC PROPERTIES OF THE RINGS OF MEASURABLE FUNCTIONS

Let M(X, \mathcal{A}, \mu) be the ring of real-valued measurable functions on a measure space (X, \mathcal{A}, \mu). In this paper, we show that the maximal ideals of M(X, \mathcal{A}, \mu) are associated with the special measurable sets in \mathcal{A}. We also study some other algebraic properties of M(X, \mathcal{A}, \mu).

کلیدواژه ها:

Measure spaces ، Rings of measurable functions ، Maximal ideals ، Prime ideals ، Variety of ideals