Algebraic structure of continuous, unbounded and integrable functions
Abstract
In this paper we study the large linear and algebraic size of the family of unbounded continuous and integrable functions in [0,+∞) and of the family of sequences of these functions converging to zero uniformly on compacta and in L1-norm. In addition, we concentrate on the speed at which these functions grow, their smoothness and the strength of their convergence to zero.
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