We would like to generalize to non-Newtonian real numbers the usual Lebesgue measure in real numbers. For this purpose, we introduce the Lebesgue measure on open and closed sets in non-Newtonian sense and examine their basic properties.

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The object of this paper is to introduce generalized Lorentz sequence spaces L(f, v, p) defined by modulus function f. Also we study some topologic properties of this space and obtain some inclusion relations.

We introduce a new space of double sequences related to -absolute convergent double sequence space, combining an Orlicz function and an infinity double matrix. We study some properties of and obtain some inclusion relations involving .

In this work we introduce new spaces 2 ( , , ) of double sequences defined by a double sequence of modulus functions, and we study some properties of this space.