Abstract
In this chapter we deal with the strong Luzin ((SL)-) integral, related with the existence of primitives of functions in the weak sense. This integral is a variant of the Kurzweil-Henstock integral, which coincides with it in the real case, but is in general slightly different in the context of Riesz spaces, because some pathologies can occur. We also prove some versions of Hake and monotone convergence type theorems and of the Fundamental Theorem of Calculus, together with the basic properties.
Related Books
Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application
Advanced Calculus - Fundamentals of Mathematics
Advanced Numerical Methods for Complex Environmental Models: Needs and Availability
An Introduction to Sobolev Spaces
An Introduction to Trigonometry and its Applications
Analysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods
Applied Computational Mathematics in Social Sciences
Calculus: The Logical Extension of Arithmetic
Complex Analyses in Engineering, Science and Technology
Convergence Theorems for Lattice Group-Valued Measures