Mathematical Sciences: Applications of Nonstandard Analysis to Measure Theory, Potential Theory, and Related Topics
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Professor Loeb is one of the world's leading experts in the                 applications of the fundamental foundational concept in                         mathematics called nonstandard analysis.  This construct, first                 introduced by logicians, is an ingenious rigorous development of                the classical concepts of infinitesimally large and small                       numbers.  Nonstandard analysis, therefore, is a mathematical                    vindication of Leibnitz' philosophical viewpoint in his invention               of the calculus.  Professor Loeb is the leading practitioner in                 the use of nonstandard methods to prove "standard" results in a                 broad range of mathematical analysis and applications.  Loeb's                  work in nonstandard measure theory and nonstandard measure theory               and nonstandard probability theory has led to important                         contributions to probability theory, mathematical physics, and                  mathematical economics.  The notion of Loeb measure, introduced                 by the principal investigator, has become a standard tool in                    probability theory, stochastic analysis, and potential theory.                  The current proposal by Professor Loeb has two parts.  First, he                proposes to combine his nonstandard integration theory with                     nonstandard convex hulls.  Applications are envisaged to Banach                 spaces and Banach space valued stochastic processes.  Secondly,                 he proposes to continue his work on the concept of ideal (Loeb)                 boundary, developed for very general potential theories.  This                  research promises to have important implications for classical                  potential theory.
{'FirstName': 'Peter', 'LastName': 'Loeb', 'PI_MID_INIT': 'A', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Peter A Loeb', 'EmailAddress': 'loeb@math.uiuc.edu', 'PI_PHON': '2173338664', 'NSF_ID': '000438015', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Illinois at Urbana-Champaign', 'CityName': 'URBANA', 'ZipCode': '618013620', 'PhoneNumber': '2173332187', 'StreetAddress': '506 S WRIGHT ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '13', 'CONGRESS_DISTRICT_ORG': 'IL13', 'ORG_UEI_NUM': 'Y8CWNJRCNN91', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ILLINOIS', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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