German Americans especially regarding pastries, meats and sausages, and above all, beer. Frankfurters (or "wieners", originating from Frankfurt am Main and Vienna, respectively), hamburgers, bratwurst, sauerkraut, and strudel are common dishes. German bakers introduced the pretzel, which is popular across the United States. Germans introduced America to lager, the most-produced beer style in the United States, and have been the dominant ethnic group in the beer industry since 1850. The oldest extant brewery in the United States is D. G. Yuengling & Son of Pottsville, Pennsylvania (approximately 80 miles northwest of Philadelphia), founded in 1829 by an immigrant from Aldingen in what
Slowly varying function if for all , . A function for which the limit is finite but nonzero for every , is called a "regularly varying function". These definitions are due to Jovan Karamata. Regularly varying functions have some important properties: a partial list of them is reported below. More extensive analyses of the properties characterizing regular variation are presented in the monograph by . . The limit in and is uniform if is restricted to a compact interval. . Every regularly varying function is of the form where Note. This implies that the function in has necessarily to be of the following