An Introduction to Probability Theory - Geiss
The modern period of probability theory is connected with names like S.N.
Be rns te in (1880-1968), E . Borel (1871- 1956), and A.N. Kolmogorov (1903-
1987). In partic ular, in 1933 A.N. Kolmogorov published his mo de rn ap-
proach of Probability Theory, including the notion of a measurable s pace
and a probability space. This lecture w ill start from this notion, to continue
with random variable s and basic parts of integration theory, and to finis h
with s ome first limit theore ms.
The lecture is bas ed on a mathematical axiomatic approach and is intende d
for students f rom mathematic s, but als o for other students who nee d more
mathe matical background for their further studies. We assume that the
integration with resp ec t to the Riemann- integral on the real line is know n.
The approach, we follow, seems to b e in the b eginning more difficult. B ut
once one has a solid basis, many things will b e easier and more transparent
late r. Le t us s tart with an intro ducing example leading us to a proble m
which should motivate our axiomatic approach.
- Pub Date: February 19, 2004
- Pages:71
The modern period of probability theory is connected with names like S.N.
Be rns te in (1880-1968), E . Borel (1871- 1956), and A.N. Kolmogorov (1903-
1987). In partic ular, in 1933 A.N. Kolmogorov published his mo de rn ap-
proach of Probability Theory, including the notion of a measurable s pace
and a probability space. This lecture w ill start from this notion, to continue
with random variable s and basic parts of integration theory, and to finis h
with s ome first limit theore ms.
The lecture is bas ed on a mathematical axiomatic approach and is intende d
for students f rom mathematic s, but als o for other students who nee d more
mathe matical background for their further studies. We assume that the
integration with resp ec t to the Riemann- integral on the real line is know n.
The approach, we follow, seems to b e in the b eginning more difficult. B ut
once one has a solid basis, many things will b e easier and more transparent
late r. Le t us s tart with an intro ducing example leading us to a proble m
which should motivate our axiomatic approach.
