Abstract
This chapter discusses the extension of positive σ- and τ-measures applying Daniell's classical method of monotone extension. In case the integral stems from σ-content prespace, the extension problem for the latter turns out to be solved there by once more. In connection with content and measure theory, three convergence concepts for functions are considered so far: point wise convergence, convergence a.e. for a given σ-measure or σ-content, and L1-norm resp. L2-norm convergence for a given σ-measure or σ-content.
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