Abstract In this work we introduce and study some concepts relatively to fuzzy σ–algebra such as measure, countably additive, complete measure extension of measure. Moreover, present their basic properties examples them. addition, it is shown that the linear combination a too. Finally, relationships between proposed have been introduced.

What follows is propaganda for the study of a particular commutative Banach algebra, A one not inappropriate to a conference which emphasises automatic continuity. In fact A is that subalgebra of the measure algebra, .i\J(T), of all regular bounded Borel measures on the circle under the total variation norm and convolution multiplication, which is characterised by the automatic continuity of me...