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Acer ES100 Driver Download Acer ES100 driverQ: Bounded convergence implies convergence in $L^p$ Let $f_n$ be a sequence of functions such that $f_n\to f$ pointwise. If for every $p \geq 1$ we have $\int |f_n|^p \to \int |f|^p$, then is it true that for all $p \geq 1$ we have $f_n \to f$ in $L^p$? A: Hint: Suppose $f\geq 0$. Suppose also that $f_n\to f$ in $L^p$ for some $p>1$. Then $\int_1^\infty \frac{f(x)^p}{x^p}\,dx=\lim\int_1^\infty \frac{f_n(x)^p}{x^p}\,dx$. Now use the dominated convergence theorem. Also: the necessary and sufficient condition is that $f_n\to f$ in $L^1$. The study began with 765 individuals enrolled in the Blount County, Alabama, Heart Health Program, a population-based, cross-sectional cardiovascular risk factor surveillance project. Participants included 437 women and 328 men aged 20--74 years. The participants in this study were residents of Blount County who were 18 years of age and older and had completed the 2006 BRFSS. Of the 10,019 individuals in the study sample, 9,987 (99%) completed the BRFSS survey. Of these, 7,947 (83%) completed the tobacco use module and had valid data on smoking status, and 5435 (57%) completed the BP and lipid profile. The authors thank the BRFSS staff at the Alabama Department of Public Health for their assistance with the BRFSS. Authors' disclosures available online ()

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