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Creator: Uhlig, Harald, 1961 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) Number: 342 Abstract: [Please note that the following Greek lettering is improperly transcribed.] If [0,1] is a measure space of agents and X a collection of pairwise uncorrelated random variables with common finite mean U and variance a , one would like to establish a law of large numbers () Xdl = U. In this paper we propose to interpret () as a Pettis integral. Using the corresponding Riemanntype version of this integral, we establish (*) and interpret it as an L2law of large numbers. Intuitively, the main idea is to integrate before drawing an W, thus avoiding wellknow measurability problems. We discuss distributional properties of i.i.d. random shocks across the population. We given examples for the economic interpretability of our definition. Finally, we establish a vectorvalued version of the law of large numbers for economies.
Keyword: Random variable, Khinchines law of large numbers, L2 law of large numbers, Riemann integral, Pettis integral, and Large numbers Subject (JEL): C10  Econometric and statistical methods : General  General 
Creator: Uhlig, Harald, 1961 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) Number: 342 Abstract: [Please note that the following Greek lettering is improperly transcribed.] If [0,1] is a measure space of agents and X a collection of pairwise uncorrelated random variables with common finite mean U and variance a , one would like to establish a law of large numbers () Xdl = U. In this paper we propose to interpret () as a Pettis integral. Using the corresponding Riemanntype version of this integral, we establish (*) and interpret it as an L2law of large numbers. Intuitively, the main idea is to integrate before drawing an W, thus avoiding wellknow measurability problems. We discuss distributional properties of i.i.d. random shocks across the population. We given examples for the economic interpretability of our definition. Finally, we establish a vectorvalued version of the law of large numbers for economies.
Keyword: Random variable, Khinchines law of large numbers, L2 law of large numbers, Riemann integral, Pettis integral, and Large numbers Subject (JEL): C10  Econometric and statistical methods : General  General