RUANG MATRIX LINEAR TRANSLASI INVARIAN PADA RUANG FUNGSI INTEGRAL HENSTOCK-DUNFORD PADA [a,b] - Solikhin, Solikhin; Sumanto, YD; Hariyanto, Susilo; Aziz, Abdul (MATEMATIKA, 2017)
In this paper we study Henstock-Dunford integral on [a,b]. We discuss some properties of the integrable. We will construct norm and matrix on Dunford-Henstock integrable function space, HD[a,b]. We obtain that HD[a,b] is linear space. A function \| . \|:HD[a,b]→ R defined by \| f \|=smallmatrix x^*X^* \| x^* \| 1 smallmatrix left( A[a,b] | ( H ) _Ax^*f | ) for every f HD[a,b] is norm on linear space HD[a,b]. A function d:HD[a,b]× HD[a,b]→ R defined by d( f,g )=\| f-g \| for every f,gHD[a,b] is a matrix on linear space HD[a,b]. Further more, linear space HD[a,b] is linear matrix translation invarian space.