UToronto

Jul
2
awarded Curious
May
8
awarded Popular Question
Apr
11
awarded Yearling
Apr
11
awarded Yearling
May
7
awarded Tumbleweed
Apr
30
accepted Constructing a Measure from a Function
Apr
30
revised Image of Thom Class under Sequence of Maps?
added 425 characters in body
Apr
30
asked Image of Thom Class under Sequence of Maps?
Dec
14
accepted Relationship between the $2$-plane bundles over $S^2$ and $\mathbb{Z}$
Dec
1
accepted Periodic Solutions for a System
Nov
30
comment Periodic Solutions for a System
That certainly makes a lot more sense now. Is there a way from that new system to get our periodic solutions? I'm probably missing something easy here, but I'm a bit forgetful on how to solve it.
Nov
30
revised Periodic Solutions for a System
added 57 characters in body
Nov
30
asked Periodic Solutions for a System
Nov
15
comment Constructing a Measure from a Function
Thanks for the clear explanation! That made perfect sense.
Nov
15
comment Constructing a Measure from a Function
Other than using my "interval jumping argument", what's a clearer way to explain that $G_N(x)=\sum_{n=1}^N a_n1_{[c_n,\infty)}(x)$ is right-continuous? It seems that when I try to explain that this is right-continuous, it uses the same logic as showing that the desired function is right-continuous in the first place. I am a fan of that clever use of the indicator function though!
Nov
15
comment Constructing a Measure from a Function
Actually, it does seem this argument is still valid. I can just replace $c_{n+1}$ with the condition that it holds for every $c_i>c_n$. That is, the function remains constant for all $x$ where $c_n\leq x<c_i$ for all $c_i>c_n$. Then the constant interval would jump to another when $x$ reaches one of these $c_i$'s.
Nov
15
revised Constructing a Measure from a Function
added 46 characters in body
Nov
15
comment Constructing a Measure from a Function
Note that the function/summation remains constant for all $x$ where $c_n\leq x < c_{n+1}$. It then "jumps" to the next interval when $x=c_{n+1}$. That is, the function is basically just intervals jumping to the next, where each interval is closed on the left. (as in en.wikipedia.org/wiki/File:Right-continuous.svg) Actually, I'm not too sure if this argument works because I'm assuming that the $c_n$'s are non-decreasing. Could I somehow build an analogous argument by re-ordering the $c_n$'s or doing something similar?
Nov
15
revised Constructing a Measure from a Function
added 37 characters in body
Nov
15
asked Constructing a Measure from a Function
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